Physics Book - User contributions [en]

Change of State

2023-04-12T02:43:57Z

Kmanek3:

Edited by Krishi Manek (Spring 2023)

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

===An Overview===

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

===Solid/Liquid===

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

===Liquid/Gas===

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter2.jpeg]]

===Solid/ Gas===
Sublimation occurs when a substance goes from a solid state directly to a gaseous state, without passing through the liquid state. This process happens when the temperature and pressure conditions are such that the vapor pressure of the solid substance exceeds the ambient pressure. As the solid is heated, its vapor pressure increases until it equals the ambient pressure, at which point the substance begins to sublimate and turn into a gas. Examples of substances that can undergo sublimation include dry ice (solid carbon dioxide), mothballs (naphthalene), and frozen air fresheners (para-dichlorobenzene).

Deposition, on the other hand, is the reverse process of sublimation, where a gas transforms directly into a solid, without passing through the liquid phase. This process occurs when a gas is cooled to a temperature below its sublimation point, at which point it starts to deposit onto a solid surface. Examples of deposition include the formation of frost on a cold surface, the formation of snow from water vapor in the atmosphere, and the deposition of solid carbon dioxide (also known as "dry ice") from gaseous carbon dioxide.

Both sublimation and deposition are important physical processes that play a role in many natural phenomena and industrial applications. For example, sublimation is used in freeze-drying of foods and medicines, while deposition is involved in the formation of snowflakes and other forms of precipitation.

===Phase Change Diagram===
[[File:State_change.jpeg]]

===Heating Curve===

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

===Phase Diagram===

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

However, this model is to be used with the caveat that it only works when the matter is in a fixed state i.e. it cannot be applied during state changes such as freezing/ melting and evaporation/ condensation. Instead, the idea of "latent heat" can be used during the change of state.

Latent heat refers to the amount of heat energy required or released during a phase change of a substance, such as melting, freezing, vaporization, or condensation. This energy is used to break or form the intermolecular bonds between the particles of the substance, rather than to increase or decrease the temperature of the substance.

The amount of latent heat involved in a phase change depends on the specific substance and the conditions under which the phase change occurs. The equations used to compute latent heat can vary depending on the specific context, but here are some common ones:

Latent heat of fusion (melting or freezing):
The amount of heat energy required to change the state of a substance from a solid to a liquid or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of fusion for the substance.

Latent heat of vaporization (boiling or condensation):
The amount of heat energy required to change the state of a substance from a liquid to a gas or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of vaporization for the substance.

These equations assume that the phase change occurs at constant temperature, which is often the case under normal conditions. However, if the temperature is changing during the phase change, additional equations and considerations may be necessary to accurately calculate the latent heat involved.

===Glowscript Code===
The following Glowscript code creates a simple system of particles that can exist in three different states: solid, liquid, or gas. The particles are represented by spheres, and their behavior is determined by the current state of the system. The simulation loop updates the positions and velocities of the particles based on the current state, and checks for state transitions based on the positions of the particles.

Note that this is a very basic example, and there are many ways to expand on this code to create more complex simulations of states of matter.

[https://trinket.io/glowscript/0f31f6b4c0]

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==Other States==
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

File:States of matter2.jpeg

2023-04-12T02:43:41Z

Kmanek3:

Change of State

2023-04-12T02:39:40Z

Kmanek3:

Edited by Krishi Manek (Spring 2023)

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

===An Overview===

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

===Solid/Liquid===

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

===Liquid/Gas===

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

===Solid/ Gas===
Sublimation occurs when a substance goes from a solid state directly to a gaseous state, without passing through the liquid state. This process happens when the temperature and pressure conditions are such that the vapor pressure of the solid substance exceeds the ambient pressure. As the solid is heated, its vapor pressure increases until it equals the ambient pressure, at which point the substance begins to sublimate and turn into a gas. Examples of substances that can undergo sublimation include dry ice (solid carbon dioxide), mothballs (naphthalene), and frozen air fresheners (para-dichlorobenzene).

Deposition, on the other hand, is the reverse process of sublimation, where a gas transforms directly into a solid, without passing through the liquid phase. This process occurs when a gas is cooled to a temperature below its sublimation point, at which point it starts to deposit onto a solid surface. Examples of deposition include the formation of frost on a cold surface, the formation of snow from water vapor in the atmosphere, and the deposition of solid carbon dioxide (also known as "dry ice") from gaseous carbon dioxide.

Both sublimation and deposition are important physical processes that play a role in many natural phenomena and industrial applications. For example, sublimation is used in freeze-drying of foods and medicines, while deposition is involved in the formation of snowflakes and other forms of precipitation.

===Phase Change Diagram===
[[File:State_change.jpeg]]

===Heating Curve===

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

===Phase Diagram===

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

However, this model is to be used with the caveat that it only works when the matter is in a fixed state i.e. it cannot be applied during state changes such as freezing/ melting and evaporation/ condensation. Instead, the idea of "latent heat" can be used during the change of state.

Latent heat refers to the amount of heat energy required or released during a phase change of a substance, such as melting, freezing, vaporization, or condensation. This energy is used to break or form the intermolecular bonds between the particles of the substance, rather than to increase or decrease the temperature of the substance.

The amount of latent heat involved in a phase change depends on the specific substance and the conditions under which the phase change occurs. The equations used to compute latent heat can vary depending on the specific context, but here are some common ones:

Latent heat of fusion (melting or freezing):
The amount of heat energy required to change the state of a substance from a solid to a liquid or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of fusion for the substance.

Latent heat of vaporization (boiling or condensation):
The amount of heat energy required to change the state of a substance from a liquid to a gas or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of vaporization for the substance.

These equations assume that the phase change occurs at constant temperature, which is often the case under normal conditions. However, if the temperature is changing during the phase change, additional equations and considerations may be necessary to accurately calculate the latent heat involved.

===Glowscript Code===
The following Glowscript code creates a simple system of particles that can exist in three different states: solid, liquid, or gas. The particles are represented by spheres, and their behavior is determined by the current state of the system. The simulation loop updates the positions and velocities of the particles based on the current state, and checks for state transitions based on the positions of the particles.

Note that this is a very basic example, and there are many ways to expand on this code to create more complex simulations of states of matter.

[https://trinket.io/glowscript/0f31f6b4c0]

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==Other States==
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

Change of State

2023-04-12T02:39:03Z

Kmanek3:

Edited by Krishi Manek (Spring 2023)

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

===An Overview===

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

===Solid/Liquid===

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

===Liquid/Gas===

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

===Solid/ Gas===
Sublimation occurs when a substance goes from a solid state directly to a gaseous state, without passing through the liquid state. This process happens when the temperature and pressure conditions are such that the vapor pressure of the solid substance exceeds the ambient pressure. As the solid is heated, its vapor pressure increases until it equals the ambient pressure, at which point the substance begins to sublimate and turn into a gas. Examples of substances that can undergo sublimation include dry ice (solid carbon dioxide), mothballs (naphthalene), and frozen air fresheners (para-dichlorobenzene).

Deposition, on the other hand, is the reverse process of sublimation, where a gas transforms directly into a solid, without passing through the liquid phase. This process occurs when a gas is cooled to a temperature below its sublimation point, at which point it starts to deposit onto a solid surface. Examples of deposition include the formation of frost on a cold surface, the formation of snow from water vapor in the atmosphere, and the deposition of solid carbon dioxide (also known as "dry ice") from gaseous carbon dioxide.

Both sublimation and deposition are important physical processes that play a role in many natural phenomena and industrial applications. For example, sublimation is used in freeze-drying of foods and medicines, while deposition is involved in the formation of snowflakes and other forms of precipitation.

===Phase Change Diagram===
[[File:State_change.jpg]]

===Heating Curve===

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

===Phase Diagram===

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

However, this model is to be used with the caveat that it only works when the matter is in a fixed state i.e. it cannot be applied during state changes such as freezing/ melting and evaporation/ condensation. Instead, the idea of "latent heat" can be used during the change of state.

Latent heat refers to the amount of heat energy required or released during a phase change of a substance, such as melting, freezing, vaporization, or condensation. This energy is used to break or form the intermolecular bonds between the particles of the substance, rather than to increase or decrease the temperature of the substance.

The amount of latent heat involved in a phase change depends on the specific substance and the conditions under which the phase change occurs. The equations used to compute latent heat can vary depending on the specific context, but here are some common ones:

Latent heat of fusion (melting or freezing):
The amount of heat energy required to change the state of a substance from a solid to a liquid or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of fusion for the substance.

Latent heat of vaporization (boiling or condensation):
The amount of heat energy required to change the state of a substance from a liquid to a gas or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of vaporization for the substance.

These equations assume that the phase change occurs at constant temperature, which is often the case under normal conditions. However, if the temperature is changing during the phase change, additional equations and considerations may be necessary to accurately calculate the latent heat involved.

===Glowscript Code===
The following Glowscript code creates a simple system of particles that can exist in three different states: solid, liquid, or gas. The particles are represented by spheres, and their behavior is determined by the current state of the system. The simulation loop updates the positions and velocities of the particles based on the current state, and checks for state transitions based on the positions of the particles.

Note that this is a very basic example, and there are many ways to expand on this code to create more complex simulations of states of matter.

[https://trinket.io/glowscript/0f31f6b4c0]

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==Other States==
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

File:State change.jpeg

2023-04-12T02:38:32Z

Kmanek3:

Change of State

2023-04-12T02:35:28Z

Kmanek3:

Edited by Krishi Manek (Spring 2023)

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

===An Overview===

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

===Solid/Liquid===

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

===Liquid/Gas===

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

===Solid/ Gas===
Sublimation occurs when a substance goes from a solid state directly to a gaseous state, without passing through the liquid state. This process happens when the temperature and pressure conditions are such that the vapor pressure of the solid substance exceeds the ambient pressure. As the solid is heated, its vapor pressure increases until it equals the ambient pressure, at which point the substance begins to sublimate and turn into a gas. Examples of substances that can undergo sublimation include dry ice (solid carbon dioxide), mothballs (naphthalene), and frozen air fresheners (para-dichlorobenzene).

Deposition, on the other hand, is the reverse process of sublimation, where a gas transforms directly into a solid, without passing through the liquid phase. This process occurs when a gas is cooled to a temperature below its sublimation point, at which point it starts to deposit onto a solid surface. Examples of deposition include the formation of frost on a cold surface, the formation of snow from water vapor in the atmosphere, and the deposition of solid carbon dioxide (also known as "dry ice") from gaseous carbon dioxide.

Both sublimation and deposition are important physical processes that play a role in many natural phenomena and industrial applications. For example, sublimation is used in freeze-drying of foods and medicines, while deposition is involved in the formation of snowflakes and other forms of precipitation.

===Phase Change Diagram===
[[File:State_change_diagram.jpg]]

===Heating Curve===

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

===Phase Diagram===

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

However, this model is to be used with the caveat that it only works when the matter is in a fixed state i.e. it cannot be applied during state changes such as freezing/ melting and evaporation/ condensation. Instead, the idea of "latent heat" can be used during the change of state.

Latent heat refers to the amount of heat energy required or released during a phase change of a substance, such as melting, freezing, vaporization, or condensation. This energy is used to break or form the intermolecular bonds between the particles of the substance, rather than to increase or decrease the temperature of the substance.

The amount of latent heat involved in a phase change depends on the specific substance and the conditions under which the phase change occurs. The equations used to compute latent heat can vary depending on the specific context, but here are some common ones:

Latent heat of fusion (melting or freezing):
The amount of heat energy required to change the state of a substance from a solid to a liquid or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of fusion for the substance.

Latent heat of vaporization (boiling or condensation):
The amount of heat energy required to change the state of a substance from a liquid to a gas or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of vaporization for the substance.

These equations assume that the phase change occurs at constant temperature, which is often the case under normal conditions. However, if the temperature is changing during the phase change, additional equations and considerations may be necessary to accurately calculate the latent heat involved.

===Glowscript Code===
The following Glowscript code creates a simple system of particles that can exist in three different states: solid, liquid, or gas. The particles are represented by spheres, and their behavior is determined by the current state of the system. The simulation loop updates the positions and velocities of the particles based on the current state, and checks for state transitions based on the positions of the particles.

Note that this is a very basic example, and there are many ways to expand on this code to create more complex simulations of states of matter.

[https://trinket.io/glowscript/0f31f6b4c0]

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==Other States==
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

File:State change diagram.jpg

2023-04-12T02:34:30Z

Kmanek3:

Change of State

2023-04-12T02:24:45Z

Kmanek3:

Edited by Krishi Manek (Spring 2023)

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

'''An Overview'''

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

'''Solid/Liquid'''

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

'''Liquid/Gas'''

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

'''Heating Curve'''

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

'''Phase Diagram'''

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

However, this model is to be used with the caveat that it only works when the matter is in a fixed state i.e. it cannot be applied during state changes such as freezing/ melting and evaporation/ condensation. Instead, the idea of "latent heat" can be used during the change of state.

Latent heat refers to the amount of heat energy required or released during a phase change of a substance, such as melting, freezing, vaporization, or condensation. This energy is used to break or form the intermolecular bonds between the particles of the substance, rather than to increase or decrease the temperature of the substance.

The amount of latent heat involved in a phase change depends on the specific substance and the conditions under which the phase change occurs. The equations used to compute latent heat can vary depending on the specific context, but here are some common ones:

Latent heat of fusion (melting or freezing):
The amount of heat energy required to change the state of a substance from a solid to a liquid or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of fusion for the substance.

Latent heat of vaporization (boiling or condensation):
The amount of heat energy required to change the state of a substance from a liquid to a gas or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of vaporization for the substance.

These equations assume that the phase change occurs at constant temperature, which is often the case under normal conditions. However, if the temperature is changing during the phase change, additional equations and considerations may be necessary to accurately calculate the latent heat involved.

===Glowscript Code===
The following Glowscript code creates a simple system of particles that can exist in three different states: solid, liquid, or gas. The particles are represented by spheres, and their behavior is determined by the current state of the system. The simulation loop updates the positions and velocities of the particles based on the current state, and checks for state transitions based on the positions of the particles.

Note that this is a very basic example, and there are many ways to expand on this code to create more complex simulations of states of matter.

[https://trinket.io/glowscript/0f31f6b4c0]

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==Other States==
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

Change of State

2023-04-12T02:24:36Z

Kmanek3:

Claimed by Krishi Manek (Spring 2023)

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

'''An Overview'''

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

'''Solid/Liquid'''

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

'''Liquid/Gas'''

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

'''Heating Curve'''

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

'''Phase Diagram'''

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

However, this model is to be used with the caveat that it only works when the matter is in a fixed state i.e. it cannot be applied during state changes such as freezing/ melting and evaporation/ condensation. Instead, the idea of "latent heat" can be used during the change of state.

Latent heat refers to the amount of heat energy required or released during a phase change of a substance, such as melting, freezing, vaporization, or condensation. This energy is used to break or form the intermolecular bonds between the particles of the substance, rather than to increase or decrease the temperature of the substance.

The amount of latent heat involved in a phase change depends on the specific substance and the conditions under which the phase change occurs. The equations used to compute latent heat can vary depending on the specific context, but here are some common ones:

Latent heat of fusion (melting or freezing):
The amount of heat energy required to change the state of a substance from a solid to a liquid or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of fusion for the substance.

Latent heat of vaporization (boiling or condensation):
The amount of heat energy required to change the state of a substance from a liquid to a gas or vice versa at constant temperature is given by the equation:
Q = mL

where Q is the amount of heat energy required or released, m is the mass of the substance, and L is the latent heat of vaporization for the substance.

These equations assume that the phase change occurs at constant temperature, which is often the case under normal conditions. However, if the temperature is changing during the phase change, additional equations and considerations may be necessary to accurately calculate the latent heat involved.

===Glowscript Code===
The following Glowscript code creates a simple system of particles that can exist in three different states: solid, liquid, or gas. The particles are represented by spheres, and their behavior is determined by the current state of the system. The simulation loop updates the positions and velocities of the particles based on the current state, and checks for state transitions based on the positions of the particles.

Note that this is a very basic example, and there are many ways to expand on this code to create more complex simulations of states of matter.

[https://trinket.io/glowscript/0f31f6b4c0]

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==Other States==
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

Change of State

2023-04-11T20:54:47Z

Kmanek3:

Claimed by Krishi Manek (Spring 2023)

Short Description of Topic

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

'''An Overview'''

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

'''Solid/Liquid'''

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

'''Liquid/Gas'''

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

'''Heating Curve'''

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

'''Phase Diagram'''

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==Other States==
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

Change of State

2023-04-11T20:53:22Z

Kmanek3:

Claimed by Krishi Manek (Spring 2023)

Short Description of Topic

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

'''An Overview'''

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

'''Solid/Liquid'''

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

'''Liquid/Gas'''

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

'''Heating Curve'''

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

'''Phase Diagram'''

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

'''Other States'''
Here is some useful information on the two states of matter not discussed above, namely plasma and the Bose-Einstein condensate.
Plasma:
It is a highly ionized gas that contains a significant number of free electrons and positive ions.

Plasma can be created by heating a gas to high temperatures, applying an electric field to a gas, or exposing a gas to intense radiation. This causes some of the gas particles to become ionized, meaning they lose or gain electrons, and become highly charged.

Plasma has some unique properties that distinguish it from the other states of matter. For example, it can conduct electricity and generate magnetic fields, making it useful for applications such as fusion reactors, plasma cutting, and plasma TVs.

Plasma is also the most common state of matter in the universe, as it makes up over 99% of visible matter, including stars and galaxies.

Bose-Einstein Condensate:
It is a state of matter that occurs at extremely low temperatures, close to absolute zero (-273.15°C or 0 Kelvin). It is named after Satyendra Nath Bose and Albert Einstein, who first predicted its existence in 1924-1925.

BEC is a state of matter in which a group of bosons (particles that follow Bose-Einstein statistics) collapse into the same quantum state, forming a single macroscopic entity. This means that all the atoms making up the BEC behave as a single entity, rather than as individual atoms.

BEC was first observed experimentally in 1995, when researchers at the University of Colorado and the National Institute of Standards and Technology were able to cool a gas of rubidium atoms to near absolute zero, causing them to collapse into a single quantum state.

BEC has some unique properties that distinguish it from other states of matter. For example, it exhibits wave-like properties and can form interference patterns, similar to the behavior of light waves. It is also incredibly sensitive to external stimuli, such as magnetic and electric fields, making it useful for precision measurements and the development of new technologies such as atom lasers.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

Change of State

2023-04-11T20:48:25Z

Kmanek3:

Claimed by Krishi Manek (Spring 2023)

Short Description of Topic

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

'''An Overview'''

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

'''Solid/Liquid'''

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

'''Liquid/Gas'''

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:States_of_matter.jpeg]]

'''Other States'''

Transitions into the two lesser known states are much harder to analyze and understand. As these states are only present under extreme and unique conditions they will not be discussed in depth. There are links below for further reading on these topics.

'''Heating Curve'''

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

'''Phase Diagram'''

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

File:States of matter.jpeg

2023-04-11T20:47:50Z

Kmanek3:

Change of State

2023-04-11T20:47:19Z

Kmanek3:

Claimed by Krishi Manek (Spring 2023)

Short Description of Topic

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

'''An Overview'''

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy between the matter and its surroundings during such a transition - either the matter absorbs energy, or it releases energy to transition between states.

'''Solid/Liquid'''

A very common phase change is between liquid and solids. When a liquid is converted to a solid, this change of state is referred to as ''freezing'', and it is an exothermic reaction i.e. it releases heat, warming up its surroundings.
Conversely, when a solid is converted to a liquid, this change of state is referred to as ''melting/liquefaction'' and it is an endothermic reaction i.e. it absorbs heat from the surroundings, making them cooler.

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

'''Liquid/Gas'''

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

[[File:states_of_matter.jpeg]]

'''Other States'''

Transitions into the two lesser known states are much harder to analyze and understand. As these states are only present under extreme and unique conditions they will not be discussed in depth. There are links below for further reading on these topics.

'''Heating Curve'''

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

'''Phase Diagram'''

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

Change of State

2023-04-11T20:36:02Z

Kmanek3:

Claimed by Krishi Manek (Spring 2023)

Short Description of Topic

==The Main Idea==

All matter can move from one state to another under the right conditions. Depending on the properties of the matter changing states may require extreme temperature or pressure however it can be done. There are five different states of matter; gas, liquid, solid, plasma, and Bose-Einstein condensate.[http://www.livescience.com/46506-states-of-matter.html] The main idea of this wiki page is to discuss the properties of matter as it transitions between different states and how this relates to energy transfer.

'''An Overview'''

All matter can transition between the states dependent on its intrinsic properties. During these transitions there is a large change on the microscopic and macroscopic level of the matter. There is also typically a transfer of energy either into of from the matter undergoing the change.

'''Solid/Liquid'''

A very common phase change is between liquid and solids. This change of state is referred to as ''freezing'' (liquid to solid) or ''melting/fusion'' (solid to liquid).

''So what is going on a microscopic level?''

In a solid the atoms and molecules are packed tightly together. This tightly packed arrangement does not allow for much movement between the particles. Therefore a solid has low kinetic energy. In the liquid phase the particles of a substance have more kinetic energy that those in a solid. The atoms and molecules have more movement resulting in a higher kinetic energy.
In the change of state from solid to liquid there is energy required to overcome the binding forces that maintain its solid structure. This energy is called the heat of fusion.
In the change of state from liquid to solid energy is given off. The energy given off by this transition is the same amount as the energy required to freeze the matter.

'''Liquid/Gas'''

A very common phase change is between liquid and gases. This change of state is referred to as ''vaporization/boiling'' (liquid to gas) or ''condensation'' (gas to liquid).

''So what is going on a microscopic level?''

In a liquid the atoms and molecules are moving less than they would in the gas state. Therefore the gaseous state has a higher kinetic energy than the liquid state. This is due to the fact that atoms and molecules in liquids are still packed together more closely than the atoms and molecules in a gas.
In the change of state from liquid to gas there is energy required to overcome the bonds between the more closely packed atoms and molecules. This energy is called the heat of vaporization.
In the change of state from gas to liquid energy is given off by the transition. This energy is equal in magnitude to the energy required to transition from liquid to gas.

'''Other States'''

Transitions into the two lesser known states are much harder to analyze and understand. As these states are only present under extreme and unique conditions they will not be discussed in depth. There are links below for further reading on these topics.

'''Heating Curve'''

A common form of depicting the temperature at which a substance changes states and also how much heat is required to change state is a heating curve. The heating curve for water is shown below.

[[File:Heating_Curve.jpg]]

Note that at the point in which the liquid changes state there is no change in temperature. This is because the heat applied is going towards changing the bond structure of the matter and not towards heating the substance.

'''Phase Diagram'''

A common form of depicting the relationship between pressure, temperature, and the state of a substance is in a phase diagram. The phase diagram for water is shown below.

[[File:Phase_Diagram.jpg]]

Note that there is the boundary lines which denote and which temperature and pressure changes in state will occur.

===A Mathematical Model===

There are multiple different ways of modeling changes in state mathematically. The most common form is using the equations

''' <math> Q = m \cdot c \cdot \Delta T </math> and <math> Q = m \cdot H </math> (Heat of Fusion/Vaporization)'''

m = mass of substance
n = moles of substance
c = specific heat of substance

As shown in the heating curve above, these equations are used interchangeably depending on what the final and initial temperature the substance will be at.

===A Computational Model===

The concept of state change is a complex and interesting idea that is fundamental to a specialized field of physics known as statistical mechanics. In this field, the central model that describes a general mechanism of state change on the particle level is the Ising Model which utilizes Monte Carlo sampling of particles at certain temperatures in a distribution and assigns these particles a spin of either +1 or -1. The Ising Model is a simple, yet descriptive, simulation of energy state configurations in an “n by n” lattice of spins, with each “spin” being pointed in upwards (+1) or downwards (-1). The direction of the spin indicates a unique energy state of that spin.

Below is a sample simulation created in MATLAB that plots energy dependencies on normalized temperature. To run the simulation, you will need to download the files via the link provided below containing all source code. You will also need MATLAB in order to run the simulation. Make sure to only run the final_program.m file! It relies on the multiple helper functions that are associated with the Ising Model program (i.e. there is no need to run the other helper functions individually. ONLY run the final_program.m file!).

[https://drive.google.com/drive/folders/1ynOsjdaCjinBkIlCYk1XF5haeyKCrMta?usp=sharing]

Source: MATLAB (MathWorks)

If you run the simulation, the output should look similar to this plot:

[[Image:Ising_output.JPG |950px]]

While the output will be next to identical, there are actually slight differences in the actual values of temperature and energy of the species simulated. This is because Monte Carlo sampling was used, so each run is fed with randomly selected spins/temperatures and thus is independent of any other run.

==Examples==

===Simple===
'''1) What is the heat needed to melt 3g of ice?'''

<math> Q = m \cdot H </math>
Heat of Fusion for water= 334 J/g°C [http://www.kentchemistry.com/links/Energy/HeatFusion.htm]
Q= 3(334) = 1002 J

===Middling===
'''1) Calculate the heat needed/given off when 20g of water at 52°C is cooled to 27°C'''

Q=mcΔT
Specific Heat of Water= 4.184J/g°C [https://water.usgs.gov/edu/heat-capacity.html]

Q= 20(4.184)(27-52)= -2092 J
This means that 2092 J are given off by this process.

===Difficult===
'''1) Calculate the heat needed to heat 30 g of water from -1°C to 78°C'''

You have to break this problem into multiple different steps.

First you calculate the Q from the change in temperature to get it to 0°C.
Q1=mcΔT
Q1=30(4.184)(0-(-1))= 125.52J

Then you calculate the Q from the phase change
Q2=mH
Q2= 30(334) = 10020 J

First you calculate the Q from the change in temperature to get it to 78°C.
Q3=mcΔT
Q3=30(4.184)(78-0)= 9790.56J

Then you add all the Q's together
Q1 +Q2 +Q3= 125.52+10020+9790.56= 19936.08

==Connectedness==

This topic is related to all aspects of everyday life, phase changes are present in multiple different engineering processes. It is important to know where the energy is flowing in these changes of state in order to maximize efficiency. This is applicable to my major as a Biomedical Engineer because there are multiple processes which have changes of state and in order to keep a system balanced there has to be an influx or outflow of energy.

==History==

Changes of states of matter have been studied from the very beginning of the studies of science. From cooking to food and beverage preservation to the hydrological cycle, change of state is a pivotal concept in physics, especially when considering its implications for many related fields. The relation of state change to temperature, or average kinetic energy, is an important one with many historical examples. For instance, the failure of NASA managers to consider the temperature limits of the rubber O-rings on the solid rocket boosters when covered with water in sub-freezing temperatures led to the escape of super-heated gas that inevitably ignited the external tank, leading to the death of all seven astronauts on board the Space Shuttle Challenger. Although a fairly simple concept, the applications of the science behind state change go far beyond the surface and, in many cases, are crucial to the success of projects such as the space shuttle program, one that had to deal with environments (like entry to space/LEO) where state change was common, frequent, and hard to control/adapt to.

===Further reading===

More on a mathematical model
http://www.math.utk.edu/~vasili/475/Handouts/3.PhChgbk.1+title.pdf

===External links===

https://ch301.cm.utexas.edu/section2.php?target=thermo/enthalpy/heat-curves.html

https://craigssenseofwonder.wordpress.com/tag/phase-diagram/

http://www.chem4kids.com/files/matter_changes.html

http://www.livescience.com/46506-states-of-matter.html

http://www.ck12.org/chemistry/Multi-Step-Problems-with-Changes-of-State/lesson/Multi-Step-Problems-with-Changes-of-State-CHEM/

==References==

[[Category:Which Category did you place this in?]]

Main Page

2023-04-11T20:32:45Z

Kmanek3: /* Week 5 */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
*[[Classical Physics]]
</div>
</div>

[[Category:Which Category did you place this in?]]

===Weeks 2 and 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity and the Lorentz Transformation====
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Lorentz Transformations]]
*[[Relativistic Doppler Effect]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons and the Photoelectric Effect====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Weeks 5 and 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves and Wave-Particle Duality====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
*[[Fourier Series and Transform]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[The Born Rule]]
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Quantum Harmonic Oscillator]]
*[[Solution for Simple Harmonic Oscillator]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
*[[Molecules]]
*[[Covalent Bonds]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Application of Statistics in Physics]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Temperature & Entropy]]
</div>
</div>

===Additional Topics===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2023-04-11T20:31:53Z

Kmanek3: /* Properties of Matter */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
<h2><strong>Krishi Manek, Spring 2023</strong></h2>
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
*[[Classical Physics]]
</div>
</div>

[[Category:Which Category did you place this in?]]

===Weeks 2 and 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity and the Lorentz Transformation====
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Lorentz Transformations]]
*[[Relativistic Doppler Effect]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons and the Photoelectric Effect====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Weeks 5 and 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves and Wave-Particle Duality====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
*[[Fourier Series and Transform]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[The Born Rule]]
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Quantum Harmonic Oscillator]]
*[[Solution for Simple Harmonic Oscillator]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
*[[Molecules]]
*[[Covalent Bonds]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Application of Statistics in Physics]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Temperature & Entropy]]
</div>
</div>

===Additional Topics===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>