The Energy Principle: Difference between revisions

Latest revision as of 14:04, 19 April 2020

The Energy Principle
The basis of the energy principle can be described with the statement, "energy can neither be created nor destroyed." Thus, energy may only flow from one system to its surroundings. The observable universe is comprised of this system and everything else not in the system called the surroundings. The energy principle is used to describe changes in energy on a system. These energies can take numerous different forms including Kinetic Energy, Potential Energy, Chemical Energy, Rest Energy, and Thermal Energy. Creating boundaries allows for the conservation of these different types energy in that energy is not lost nor is it gained, it is simply transferred into other forms. Any energy moving over the boundaries therefore can be accounted for having been transferred from a system to its surroundings and vice versa. This notion is the core idea informing the Energy Principle: The change in energy of the system should be equal to the energy inputs from surroundings.

The Main Idea

The Energy Principle, also referred to as The First Law of Thermodynamics, defines the transfer of energy between systems. It is defined with the fact that the change of the energy of system is equal to the work surrounding in addition to heat transfers from the surroundings as well. This principle can be modeled by the equations:

(1) ΔE = Q+W
(2) ΔE_system + ΔE _surroundings = 0

You can see that these equations (particularly equation 2) describe Conservation of Energy, which is a main idea in physics, particularly in this course!

How will we use the energy principal?

In this course, we can apply the Energy Principal to many different scenarios. We can track how energy takes on different forms during an event. Whether its potential energy being turned into kinetic energy when a woman goes bungee jumping, or electrical energy turning into heat as you use your laptop, the transformation of energy can tell us a lot about a given scenario.

A basic outline for how to solve a problem using the energy principal:

(1) Determine the different types of energy associated with the problem
(2) Determine if there are values for Q and W (heat and work) associated with the problem
(3) Determine the equations for each type of energy identified
(4) Plug these into the energy equation and solve for the unknowns

Don’t worry if you’re not sure how these steps are worked out yet – you will soon!

Single Particle vs Multi Particle Systems

As with many concepts in physics, calculating the energy for the multi particle system is exactly the same as calculating the energy for a single particle system – except for the fact that you will need to account for multiple particles.

For example, If a system of one particle has a kinetic energy of 100J, then the total kinetic energy for that system is 100J. If another system consists of three particles, each with a kinetic energy of 20J, then the total kinetic energy of this system is 60J.

The same idea applies for gravitational potential energy, electric potential energy, etc.

Here is that same concept in another form:

KE_final + U_final = Work_surr + Q + KE_intial + U_initial

For a multi-particle system: E_system=(K₁+K₂+K₃+…)+(U_1,2+U_1,3+U_2,3+…)

Click here for a demonstration of the Energy Principle

Mathematical Models

These are the main equations you will be using to solve problems using the Energy Principal. We will add more equations later when describing the differing types of energy (kinetic, potential gravitational, energy of a single particle approaching the speed of light, etc) but for now, just focus on these. The Energy Principle
EQ 1: [math]\displaystyle{ {∆E} = {Q + W} }[/math] where [math]\displaystyle{ {Q} }[/math] is heat and [math]\displaystyle{ {W} }[/math] is the amount of work acting on the system.

EQ 2: [math]\displaystyle{ {∆E} = {∆K + ∆E_{Rest} + ∆U + ∆E_{Thermal}} }[/math] - the different types of energy that can be associated with a given particle in a system. Not all have to be present. These terms will vary based on the internal properties of the system being observed.

A Computational Model

These gifs demonstrate the energy principal from a Conservation of Energy standpoint. As the ball on a spring approaches the equilibrium point, the kinetic energy increases and the spring potential decreases. These values will oscillate, but the total energy will stay constant! This demonstration was written in GlowScript and iteratively updates the ball's momentum while taking into account the spring force.

Examples

Simple

Car Crash:

Two cars are in a parking lot. The first car crashes into the second car, which is initially at rest. The final kinetic energy of the first car is 50J and the final kinetic energy of the second car is 30J. What is the initial kinetic energy of the system?

Step 1: Draw the problem and write out what you know

Step 2: Apply the Energy Principle

Remember - Kinetic energy is a scalar, not a vector - express your answer as such!

Difficult

A rollercoaster with passengers has a mass of 2500kg. The rollercoaster is powered to the top of a 25m hill where it pauses for a moment at rest. It then plunges down the hill to ground level where it enters a 15m high vertical loop.

What is the speed of the rollercoaster at the top of the vertical loop?

Step One: Draw the problem out, write out the variables you know, and the one you are trying to solve.

Step 2: Apply the Energy Principle

Connectedness

One of the best ways to illustrate the Energy Principle in the real world is to imagine someone holding the ball over the top of a building. Since the person is holding the ball, the ball is not moving and has 0J of kinetic energy, however, since the ball is at its highest point, it will have its greatest potential energy because of U = mgh. Once the ball is released, the ball's velocity starts to speed up under the force of gravity, thus increasing kinetic energy. At the same time, the height of the ball is decreasing, and so is potential energy. The relationship between these, in fact, is inverse: as the value of one decreases, that of the other increases in exact proportion. Right before the ball hits the ground, its potential energy will be near zero, and its kinetic energy will be at its highest.

History

The concept of energy and its connection to the amount of work performed goes all the way back to the age of steam engines; physicists and engineers came up with this notion to determine the mechanical and thermal efficiency of their machines. In the 1850's, people like William Thomson and William Rankine began to come up with terms like 'kinetic energy' and 'potential energy' to model the different types of observed forces. After the 1920's, this study of science became to be known as thermodynamics, the science of energy transformations. This led to the laws of thermodynamics, one of which relates to the conservation of energy. William Rankine was the first to discuss the law of the conservation of energy in relation to a more general "energy principle". His discussions and work in this field defined the relationships between energy that we now consider the Energy Principle.

@@ Line 1: / Line 1: @@
-Claimed by lakshitha
-==The Energy Principle==
+'''''The Energy Principle''''' <br>
+The basis of the energy principle can be described with the statement, "energy can neither be created nor destroyed."  Thus, energy may only flow from one system to its surroundings.  The observable universe is comprised of this system and everything else not in the system called the surroundings.  The energy principle is used to describe changes in energy on a system. These energies can take numerous different forms including Kinetic Energy, Potential Energy, Chemical Energy, Rest Energy, and Thermal Energy.  Creating boundaries allows for the conservation of these different types energy in that energy is not lost nor is it gained, it is simply transferred into other forms.  Any energy moving over the boundaries therefore can be accounted for having been transferred from a system to its surroundings and vice versa.  This notion is the core idea informing the Energy Principle: The change in energy of the system should be equal to the energy inputs from surroundings. <br>
-===Background===
+== The Main Idea ==
-====A Mathematical Model====
+The Energy Principle, also referred to as The First Law of Thermodynamics, defines the transfer of energy between systems. It is defined with the fact that the change of the energy of system is equal to the work surrounding in addition to heat transfers from the surroundings as well. This principle can be modeled by the equations:
+'''(1) ΔE = Q+W '''
+<br>'''(2) ΔE<sub>system</sub> + ΔE <sub>surroundings </sub> = 0'''
+<br>You can see that these equations (particularly equation 2) describe Conservation of Energy, which is a main idea in physics, particularly in this course!
+== How will we use the energy principal? ==
+In this course, we can apply the Energy Principal to many different scenarios. We can track how energy takes on different forms during an event. Whether its potential energy being turned into kinetic energy when a woman goes bungee jumping, or electrical energy turning into heat as you use your laptop, the transformation of energy can tell us a lot about a given scenario.
+A basic outline for how to solve a problem using the energy principal:
+(1)	Determine the different types of energy associated with the problem <br>
+(2)	Determine if there are values for Q and W (heat and work) associated with the problem <br>
+(3)	Determine the equations for each type of energy identified <br>
+(4)	Plug these into the energy equation and solve for the unknowns <br>
+Don’t worry if you’re not sure how these steps are worked out yet – you will soon!
+== Single Particle vs Multi Particle Systems ==
+'''As with many concepts in physics, calculating the energy for the multi particle system is exactly the same as calculating the energy for a single particle system – except for the fact that you will need to account for multiple particles.'''
+For example, If a system of one particle has a kinetic energy of 100J, then the total kinetic energy for that system is 100J. If another system consists of three particles, each with a kinetic energy of 20J, then the total kinetic energy of this system is 60J.
+The same idea applies for gravitational potential energy, electric potential energy, etc.
+Here is that same concept in another form:
+'''KE<sub>final</sub> + U<sub>final</sub> = Work<sub>surr</sub> + Q + KE<sub>intial</sub> + U<sub>initial</sub>'''
+For a multi-particle system:
+'''E<sub>system</sub>=(K<sub>1</sub>+K<sub>2</sub>+K<sub>3</sub>+…)+(U<sub>1,2</sub>+U<sub>1,3</sub>+U<sub>2,3</sub>+…)'''
+[https://www.youtube.com/watch?v=30o4omX5qfo Click here for a demonstration of the Energy Principle]
+==Mathematical Models==
+'''These are the main equations you will be using to solve problems using the Energy Principal. We will add more equations later when describing the differing types of energy (kinetic, potential gravitational, energy of a single particle approaching the speed of light, etc) but for now, just focus on these.
+'''
+<b> The Energy Principle </b><br>
+EQ 1: <math>{∆E} = {Q + W}</math> where <math>{Q}</math> is heat and <math>{W}</math> is the amount of work acting on the system.
+EQ 2: <math>{∆E} = {∆K + ∆E_{Rest} + ∆U + ∆E_{Thermal}}</math> - the different types of energy that can be associated with a given particle in a system. Not all have to be present.  These terms will vary based on the internal properties of the system being observed.
-<math>{∆E} = {Q + W}</math>
 ====A Computational Model====
-How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
+These gifs demonstrate the energy principal from a '''Conservation of Energy''' standpoint. As the ball on a spring approaches the equilibrium point, the '''kinetic energy increases''' and the '''spring potential decreases'''. These values will '''oscillate''', but the '''total energy will stay constant'''! This demonstration was written in GlowScript and '''iteratively updates the ball's momentum''' while taking into account the spring force.
+[[File:Spring1.gif|300px]]
+[[File:Graphspring.gif]]
+==Examples==
+===Simple===
+Car Crash:
+'''Two cars are in a parking lot. The first car crashes into the second car, which is initially at rest.  The final kinetic energy of the first car is 50J and the final kinetic energy of the second car is 30J. What is the initial kinetic energy of the system?''' <br>
-===First Law===
+'''Step 1: Draw the problem and write out what you know'''<br>
+[[File:Collisionproblem1.png|300px]]
-The first law of thermodynamics defines the internal energy (E) as equal to the difference between heat transfer (Q) ''into'' a system and work (W) ''done by'' the system.  Heat removed from a system would be given a negative sign and heat applied to the system would be given a positive sign.  Internal energy can be converted into other types of energy because it acts like potential energy.  Heat and work, however, cannot be stored or conserved independently because they depend on the process.  This allows for many different possible states of a system to exist.  There can be a process known as the adiabatic process in which there is no heat transfer.  This occurs when a system is full insulated from the outside environment.  The implementation of this law also brings about another useful state variable, '''enthalpy'''.
+'''Step 2: Apply the Energy Principle''' <br>
-====A Mathematical Model====
+[[File:Collisionproblem2.jpg|300px]]
-E2 - E1 = Q - W
+Remember - Kinetic energy is a scalar, not a vector - express your answer as such!
-==Second Law==
+===Difficult===
-The second law states that there is another useful variable of heat, entropy (S).  Entropy can be described as the disorder or chaos of a system, but in physics, we will just refer to it as another variable like enthalpy or temperature.  For any given physical process, the combined entropy of a system and the environment remains a constant if the process can be reversed.  The second law also states that if the physical process is irreversible, the combined entropy of the system and the environment must increase.  Therefore, the final entropy must be greater than the initial entropy.
+A rollercoaster with passengers has a mass of 2500kg. The rollercoaster is powered to the top of a 25m hill where it pauses for a moment at rest. It then plunges down the hill to ground level where it enters a 15m high vertical loop.
-===Mathematical Models===
+What is the speed of the rollercoaster at the top of the vertical loop?
-delta S = delta Q/T
+'''Step One: Draw the problem out, write out the variables you know, and the one you are trying to solve.'''
-Sf = Si (reversible process)
-Sf > Si (irreversible process)
-===Examples===
+[[File: Physics Wiki Part 1.jpg|300px]]
-'''Reversible process''': Ideally forcing a flow through a constricted pipe, where there are no boundary layers. As the flow moves through the constriction, the pressure, volume and temperature change, but they return to their normal values once they hit the downstream.  This return to the variables' original values allows there to be no change in entropy.  It is often known as an isentropic process.
+'''Step 2: Apply the Energy Principle'''
-'''Irreversible process''': When a hot object and cold object are put in contact with each other, eventually the heat from the hot object will transfer to the cold object and the two will reach the same temperature and stay constant at that temperature, reaching equilibrium.  However, once those objects are separated, they will remain at that equilibrium temperature until something else acts upon it.  The objects do not go back to their original temperatures so there is a change in entropy.
+[[File: Physics Wiki Part 2.png|500px]]
 ==Connectedness==
-#How is this topic connected to something that you are interested in?
+One of the best ways to illustrate the Energy Principle in the real world is to imagine someone holding the ball over the top of a building. Since the person is holding the ball, the ball is not moving and has 0J of kinetic energy, however, since the ball is at its highest point, it will have its greatest potential energy because of U = mgh. Once the ball is released, the ball's velocity starts to speed up under the force of gravity, thus increasing kinetic energy. At the same time, the height of the ball is decreasing, and so is potential energy. The relationship between these, in fact, is inverse: as the value of one decreases, that of the other increases in exact proportion. Right before the ball hits the ground, its potential energy will be near zero, and its kinetic energy will be at its highest.
-#How is it connected to your major?
-#Is there an interesting industrial application?
 ==History==
-Thermodynamics was brought up as a science in the 18th and 19th centuries.  However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer.  G. Black first introduced the word 'thermodynamics'.  Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat.   The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot.  He is often known as "the father of thermodynamics".  It all began with the development of the steam engine during the Industrial Revolution.  He devised an ideal cycle of operation.  During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics.  In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics.  Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.
+The concept of energy and its connection to the amount of work performed goes all the way back to the age of steam engines; physicists and engineers came up with this notion to determine the mechanical and thermal efficiency of their machines. In the 1850's, people like William Thomson and William Rankine began to come up with terms like 'kinetic energy' and 'potential energy' to model the different types of observed forces. After the 1920's, this study of science became to be known as thermodynamics, the science of energy transformations. This led to the laws of thermodynamics, one of which relates to the conservation of energy. William Rankine was the first to discuss the law of the conservation of energy in relation to a more general "energy principle". His discussions and work in this field defined the relationships between energy that we now consider the Energy Principle.
 == See also ==
-Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?
+[[Potential Energy]]<br>
+[[Rest Mass Energy]] <br>
+[[Kinetic Energy]] <br>
+[[Work]]<br>
+[[Thermal Energy]]<br>
+[[Gravitational Potential Energy]] <br>
+[[Conservation of Energy]]<br>
+[[Spring Potential Energy]]<br>
 ===Further reading===
-Books, Articles or other print media on this topic
+Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 6
 ===External links===
-Internet resources on this topic
+http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html#coneng <br>
+http://hyperphysics.phy-astr.gsu.edu/hbase/enecon.html <br>
+https://www.youtube.com/watch?v=-tNQKn0EfBo <br>
+https://www.youtube.com/watch?v=30o4omX5qfo <br>
+https://www.youtube.com/watch?v=LNk2mUbnKus <br>
+https://www.youtube.com/watch?v=5Vfl1uX6kxM <br>
 ==References==
-https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
+http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy <br>
-http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
+http://www.texample.net/tikz/examples/earth-orbit/ <br>
-https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
+https://en.wikipedia.org/wiki/Conservation_of_energy <br>
-http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
+https://en.wikipedia.org/wiki/History_of_energy
-http://www.eoearth.org/view/article/153532/
+Chabay, Ruth W., and Bruce A. Sherwood. Matter and interactions. Hoboken: Wiley, 2015. Print.
-[[Category:Which Category did you place this in?]]
+[[Category:Energy]]

The Energy Principle: Difference between revisions

Latest revision as of 14:04, 19 April 2020

Contents

The Main Idea

How will we use the energy principal?

Single Particle vs Multi Particle Systems

Mathematical Models

A Computational Model

Examples

Simple

Difficult

Connectedness

History

See also

Further reading

External links

References

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