System & Surroundings - Revision history

Asri366 at 03:44, 17 April 2023

2023-04-17T03:44:03Z

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	~~(Ashika Srivastava (Spring 2023))~~

	==Main Idea==		==Main Idea==

Asri366 at 03:39, 17 April 2023

2023-04-17T03:39:52Z

← Older revision		Revision as of 23:39, 16 April 2023
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			(Ashika Srivastava (Spring 2023))

	==Main Idea==		==Main Idea==
	When it comes to energy, choosing what is the system versus what is the surroundings has profound effects on what needs to be accounted for when solving for various values/variables. Choosing certain objects to be a part of the system rather than the surroundings can have an extreme effect on the outcome of said variables, especially when the surroundings do a fairly large amount of work on the system.		When it comes to energy, choosing what is the system versus what is the surroundings has profound effects on what needs to be accounted for when solving for various values/variables. Choosing certain objects to be a part of the system rather than the surroundings can have an extreme effect on the outcome of said variables, especially when the surroundings do a fairly large amount of work on the system.

	By definition, a system is a specific part of the universe that we choose to study and analyze, while the surroundings are everything else that 'surrounds,' and typically has a significant effect on, the system. This page will analyze how different choices of systems can affect the components of the Energy Principle when relating it to the system.		By definition, a system is a specific part of the universe that we choose to study and analyze, while the surroundings are everything else that 'surrounds,' and typically has a significant effect on, the system. This page will analyze how different choices of systems can affect the components of the Energy Principle when relating it to the system.

			When deciding what to choose as your system versus your surroundings, it is important to look at your scenario from a very generalized point of view. For the system, look for a group or collections of parts or objects that are interacting and closed within what is called a system boundary. The system boundary helps to distinguish the system as one entity rather than many things moving at once.

	===Mathematical Model===		===Mathematical Model===
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	:While this page refers mainly to thermodynamic and energy systems, I believe the concept of systems is essential to Industrial Engineers. Industrial Engineers work on making systems as efficient as possible by minimizing waste in the production process. They also merge people, machinery, information and energy to create a product or a service. People, machinery, information and energy can be considered a system. It is an industrial engineers job to figure out the most optimal way to merge parts of the system together in order to have the greatest impact or outflow from the system to the surroundings (consumers/customers). Industrial engineers work with open systems and strive towards having a net positive outflow (i.e the resources supplied produce greater output or value).		:While this page refers mainly to thermodynamic and energy systems, I believe the concept of systems is essential to Industrial Engineers. Industrial Engineers work on making systems as efficient as possible by minimizing waste in the production process. They also merge people, machinery, information and energy to create a product or a service. People, machinery, information and energy can be considered a system. It is an industrial engineers job to figure out the most optimal way to merge parts of the system together in order to have the greatest impact or outflow from the system to the surroundings (consumers/customers). Industrial engineers work with open systems and strive towards having a net positive outflow (i.e the resources supplied produce greater output or value).

			====Chemical Engineering====

			:In addition, in regards to thermodynamic and energy systems, the concept of system & surroundings is important to Chemical Engineers. Chemical Engineers are required to accurately and efficiently identify the system they are working with in order to proceed with the necessary mass balance (and energy balance if applicable) calculations for the corresponding system. This system can be any sort of machinery, reacting plant, or even a bodily system.

	==History==		==History==

Ajanusz6 at 14:34, 18 October 2022

2022-10-18T14:34:37Z

← Older revision		Revision as of 10:34, 18 October 2022
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	==Main Idea==		==Main Idea==
	When it comes to energy, choosing what is the system versus what is the surroundings has profound ~~affects~~ on what needs to be accounted for when solving for various values/variables. Choosing certain objects to be a part of the system rather than the surroundings can have an extreme effect on the outcome of said variables, especially when the surroundings do a fairly large amount of work on the system.		When it comes to energy, choosing what is the system versus what is the surroundings has profound effects on what needs to be accounted for when solving for various values/variables. Choosing certain objects to be a part of the system rather than the surroundings can have an extreme effect on the outcome of said variables, especially when the surroundings do a fairly large amount of work on the system.

	By definition, a system is a specific part of the universe that we choose to study and analyze, while the surroundings are everything else that 'surrounds,' and typically has a significant effect on, the system. This page will analyze how different choices of systems can affect the components of the Energy Principle when relating it to the system.		By definition, a system is a specific part of the universe that we choose to study and analyze, while the surroundings are everything else that 'surrounds,' and typically has a significant effect on, the system. This page will analyze how different choices of systems can affect the components of the Energy Principle when relating it to the system.

Laurence12799: /* Difficult */

2019-07-31T20:34:12Z

Difficult

← Older revision		Revision as of 16:34, 31 July 2019
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	::We start with the Energy Principle:		::We start with the Energy Principle:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} + \~~mathbf{\vartriangle}~~E_{surroundings} = 0</math>		:::<math>\Delta E_{system} + \Delta E_{surroundings} = 0</math>

	::We want to know an expression for the Kinetic Energy of the Earth. Since the Earth is part of the system, we first want to isolate the system:		::We want to know an expression for the Kinetic Energy of the Earth. Since the Earth is part of the system, we first want to isolate the system:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} = - \~~mathbf{\vartriangle}~~E_{surroundings}</math>		:::<math>\Delta E_{system} = - \Delta E_{surroundings}</math>

	::Now, we will open up each term so that we may extract the Kinetic Energy term of the Earth:		::Now, we will open up each term so that we may extract the Kinetic Energy term of the Earth:

	:::<math>\~~mathbf{\vartriangle}~~U_{system} + \~~mathbf{\vartriangle}~~K_{system} = - \~~mathbf{\vartriangle}~~E_{surroundings}</math>		:::<math>\Delta U_{system} + \Delta K_{system} = -\Delta E_{surroundings}</math>

	:::<math>\~~mathbf{\vartriangle}~~U_{system} + \~~mathbf{\vartriangle}~~K_{Earth} + \~~mathbf{\vartriangle}~~K_{Moon} = - \~~mathbf{\vartriangle}~~E_{surroundings}</math>		:::<math>\Delta U_{system} + \Delta K_{Earth} + \Delta K_{Moon} = - \Delta E_{surroundings}</math>

	::Rearranging gives:		::Rearranging gives:

	:::<math>\~~mathbf{\vartriangle}~~K_{Earth} = - \left(\~~mathbf{\vartriangle}~~E_{surroundings} + \~~mathbf{\vartriangle}~~U_{system} + \~~mathbf{\vartriangle}~~K_{Moon} \right)</math>		:::<math>\Delta K_{Earth} = - \left(\Delta E_{surroundings} +\Delta U_{system} + \Delta K_{Moon} \right)</math>

	:'''b) With the Earth as the system, and the Moon and the Sun as the only surroundings doing work on the system, use the Energy Principle to create an expression for the Work done by the Sun on the Earth:'''		:'''b) With the Earth as the system, and the Moon and the Sun as the only surroundings doing work on the system, use the Energy Principle to create an expression for the Work done by the Sun on the Earth:'''
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	::Plugging this in gives us a way to solve for the Work done by the Sun on the Earth:		::Plugging this in gives us a way to solve for the Work done by the Sun on the Earth:

	:::<math>W_{Sun} = \~~mathbf{\vartriangle}~~E_{system} - W_{Moon}</math>		:::<math>W_{Sun} = \Delta E_{system} - W_{Moon}</math>

	:'''c) With the Sun as the system, and the Earth and the Moon as the only surroundings doing work on the system, use the Energy Principle to create an expression for the change in the Potential Energy of the Sun:'''		:'''c) With the Sun as the system, and the Earth and the Moon as the only surroundings doing work on the system, use the Energy Principle to create an expression for the change in the Potential Energy of the Sun:'''
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	::We start with the Energy Principle:		::We start with the Energy Principle:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} + \~~mathbf{\vartriangle}~~E_{surroundings} = 0</math>		:::<math>\Delta E_{system} + \Delta E_{surroundings} = 0</math>

	::From this we deduce:		::From this we deduce:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} = W</math>		:::<math>\Delta E_{system} = W</math>

	::We will extract terms from this equation to find an expression of the Potential Energy of the Sun:		::We will extract terms from this equation to find an expression of the Potential Energy of the Sun:

	:::<math>\~~mathbf{\vartriangle}~~U_{system} + \~~mathbf{\vartriangle}~~K_{system} = W_{Earth} + W_{Moon}</math>		:::<math>\Delta U_{system} + \Delta K_{system} = W_{Earth} + W_{Moon}</math>

	:::<math>\~~mathbf{\vartriangle}~~U_{system} = (W_{Earth} + W_{Moon}) - \~~mathbf{\vartriangle}~~K_{system}</math>		:::<math>\Delta U_{system} = (W_{Earth} + W_{Moon}) - \Delta K_{system}</math>

	::Since the Sun is the system, we have:		::Since the Sun is the system, we have:

	:::<math>\~~mathbf{\vartriangle}~~U_{Sun} = (W_{Earth} + W_{Moon}) - \~~mathbf{\vartriangle}~~K_{Sun}</math>		:::<math>\Delta U_{Sun} = (W_{Earth} + W_{Moon}) - \Delta K_{Sun}</math>

	==Connectedness==		==Connectedness==

Laurence12799: /* Middling */

2019-07-31T20:30:38Z

Middling

← Older revision		Revision as of 16:30, 31 July 2019
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	::'''Expressions:'''		::'''Expressions:'''

	:::<math>W = \~~mathbf{\vartriangle}~~E = \int \mathbf{F} \bullet d\mathbf{r} \ \mathbf{(1)}</math> is the equation for the work done on an object. It says the work done on an object is the equal to the change in energy of the object, which is equal to the Force applied to the object dotted with the displacement vector of the object (A Line Integral)		:::<math>W = \Delta E = \int \mathbf{F} \bullet d\mathbf{r} \ \mathbf{(1)}</math> is the equation for the work done on an object. It says the work done on an object is the equal to the change in energy of the object, which is equal to the Force applied to the object dotted with the displacement vector of the object (A Line Integral)

	:::<math>F_c = \frac{mv^2}{r} \ \mathbf{(2)}</math> is the equation relating the needed centripetal force to the object's variables		:::<math>F_c = \frac{mv^2}{r} \ \mathbf{(2)}</math> is the equation relating the needed centripetal force to the object's variables

Laurence12799: /* Simple */

2019-07-31T20:29:39Z

Simple

← Older revision		Revision as of 16:29, 31 July 2019
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	::We know in general that the change in energy of the system and its surroundings is always <math>0</math>:		::We know in general that the change in energy of the system and its surroundings is always <math>0</math>:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} + \~~mathbf{\vartriangle}~~E_{surroundings} = 0</math>		:::<math>\Delta E_{system} + \Delta E_{surroundings} = 0</math>

	::or:		::or:
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	::We can manipulate this into:		::We can manipulate this into:

	:::<math>\~~mathbf{\vartriangle}~~E_{man} = - \~~mathbf{\vartriangle}~~U_{child} - \~~mathbf{\vartriangle}~~U_{Earth} - \~~mathbf{\vartriangle}~~K_{child} - \~~mathbf{\vartriangle}~~K_{Earth}</math>		:::<math>\Delta E_{man} = -\Delta U_{child} - \Delta U_{Earth} - \Delta K_{child} -\Delta K_{Earth}</math>

	::Since the child and the man are near the surface of the Earth, using <math>mgh</math> as the gravitational potential energy for them is acceptable. Also, the Earth has no significant movement from this reference frame, since the child and man are so much less massive than it, meaning its change in gravitational potential energy is negligible and velocity is 0:		::Since the child and the man are near the surface of the Earth, using <math>mgh</math> as the gravitational potential energy for them is acceptable. Also, the Earth has no significant movement from this reference frame, since the child and man are so much less massive than it, meaning its change in gravitational potential energy is negligible and velocity is 0:

	:::<math>\~~mathbf{\vartriangle}~~E_{man} = - mg(d-0) - 0 - \frac{1}{2}m({v_f}^2 - 0) - 0</math>		:::<math>\Delta E_{man} = - mg(d-0) - 0 - \frac{1}{2}m({v_f}^2 - 0) - 0</math>

	::Simplifying gives a final answer:		::Simplifying gives a final answer:

	:::<math>\~~mathbf{\vartriangle}~~E_{man} = - \left(mgd + \frac{1}{2}m{v_f}^2\right)</math>		:::<math>\Delta E_{man} = - \left(mgd + \frac{1}{2}m{v_f}^2\right)</math>

	:'''b) Create an expression for the final velocity of the child''' (<math>v_f</math>) ''', using the Energy Principle and the child as the system, and the man and the Earth doing significant work on the system.'''		:'''b) Create an expression for the final velocity of the child''' (<math>v_f</math>) ''', using the Energy Principle and the child as the system, and the man and the Earth doing significant work on the system.'''
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	::We start as before:		::We start as before:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} + \~~mathbf{\vartriangle}~~E_{surroundings} = 0</math>		:::<math>\Delta E_{system} + \Delta E_{surroundings} = 0</math>

	:::<math>(E_{system_{f}} - E_{system_{i}}) + (E_{surroundings_{f}} - E_{surroundings_{i}}) = 0</math>		:::<math>(E_{system_{f}} - E_{system_{i}}) + (E_{surroundings_{f}} - E_{surroundings_{i}}) = 0</math>
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	::Note this time the system is just the child, and the significant surroundings (doing work) are the man and the Earth:		::Note this time the system is just the child, and the significant surroundings (doing work) are the man and the Earth:

	:::<math>\~~mathbf{\vartriangle}~~E_{child} - W + (E_{man_{f}} + E_{Earth_{f}}) - (E_{man_{i}} + E_{Earth_{I}})</math>		:::<math>\Delta E_{child} - W + (E_{man_{f}} + E_{Earth_{f}}) - (E_{man_{i}} + E_{Earth_{I}})</math>

	::Plugging in more expressions gives:		::Plugging in more expressions gives:
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	::We can simplify this by using the equation for gravitational potential energy and recognizing the terms the Earth adds are negligible. This gives:		::We can simplify this by using the equation for gravitational potential energy and recognizing the terms the Earth adds are negligible. This gives:

	:::<math>K_{child_{f}} = W - \~~mathbf{\vartriangle}~~U_{child} + K_{child_{i}} - \~~mathbf{\vartriangle}~~U_{man} - \~~mathbf{\vartriangle}~~K_{man}</math>		:::<math>K_{child_{f}} = W - \Delta U_{child} + K_{child_{i}} - \Delta U_{man} - \Delta K_{man}</math>

	::The man is still at rest in this reference frame when the child reaches a distance <math>d</math>, so his kinetic energy is 0. Furthermore, his position never changes relative to the Earth, so his change in gravitational potential energy is negligible:		::The man is still at rest in this reference frame when the child reaches a distance <math>d</math>, so his kinetic energy is 0. Furthermore, his position never changes relative to the Earth, so his change in gravitational potential energy is negligible:

	:::<math>K_{child_{f}} = W - \~~mathbf{\vartriangle}~~U_{child} + K_{child_{i}}</math>		:::<math>K_{child_{f}} = W - \Delta U_{child} + K_{child_{i}}</math>

	::Next, we know the child is at rest initially, so the initial kinetic energy of the child is 0. Also, the word done by the man will be the force times the distance:		::Next, we know the child is at rest initially, so the initial kinetic energy of the child is 0. Also, the word done by the man will be the force times the distance:

	:::<math>K_{child_{f}} = Fd - \~~mathbf{\vartriangle}~~U_{child}</math>		:::<math>K_{child_{f}} = Fd -\Delta U_{child}</math>

	::We have found that the child's kinetic energy is equal to the negative of his/her change in gravitational potential energy plus the work done by the man, which makes sense. Plugging in expressions for each side of the equation gives:		::We have found that the child's kinetic energy is equal to the negative of his/her change in gravitational potential energy plus the work done by the man, which makes sense. Plugging in expressions for each side of the equation gives:

Laurence12799: /* The Energy Principle */

2019-07-31T20:27:08Z

The Energy Principle

← Older revision		Revision as of 16:27, 31 July 2019
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	:To first understand the impact of the choice of system, it is best to fully understand the Energy Principle. The Energy Principle is based on the fact that energy is a conserved quantity in the universe, meaning that it cannot be created nor destroyed, only transferred. This definition of the conservation of energy gives us the equation:		:To first understand the impact of the choice of system, it is best to fully understand the Energy Principle. The Energy Principle is based on the fact that energy is a conserved quantity in the universe, meaning that it cannot be created nor destroyed, only transferred. This definition of the conservation of energy gives us the equation:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} + \~~mathbf{\vartriangle}~~E_{surroundings} = 0</math>		:::<math>\Delta E_{system} + \Delta E_{surroundings} = 0</math>

	:The following image best illustrates the idea that since energy is a conserved quantity, systems may only gain/lose energy if the surroundings lose/gain that same amount of energy.		:The following image best illustrates the idea that since energy is a conserved quantity, systems may only gain/lose energy if the surroundings lose/gain that same amount of energy.
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	:The Energy Principle can then be rearranged by using the fact that the change in energy of a specific system is equal to the work done on the system by the surroundings, or:		:The Energy Principle can then be rearranged by using the fact that the change in energy of a specific system is equal to the work done on the system by the surroundings, or:

	:::<math>\~~mathbf{\vartriangle}~~E_{system} = W_{surroundings}</math>, where		:::<math>\Delta E_{system} = W_{surroundings}</math>, where

	::::<math>\~~mathbf{\vartriangle}~~E_{system} = E_f - E_i</math> (The final energy of the system minus the initial energy of the system)		::::<math>\Delta E_{system} = E_f - E_i</math> (The final energy of the system minus the initial energy of the system)

	:This facts gives:		:This facts gives:

Laurence12799: /* Types of Energy Systems */

2019-07-31T20:26:35Z

Types of Energy Systems

← Older revision		Revision as of 16:26, 31 July 2019
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	::A '''Closed Energy System''' is not subject to changes in its internal energy. Therefore:		::A '''Closed Energy System''' is not subject to changes in its internal energy. Therefore:

	::::<math>\~~mathbf{\vartriangle}~~E_{system} = 0</math>		::::<math>\Delta E_{system} = 0</math>

	::Although energy transfers between the system and surroundings exist, the amount of energy inflow is equal to the amount of energy outflow, and therefore the net change in energy is equal to zero. An example of a closed system could be a thermos flask. If ice cubes and boiling water are placed into the thermos at the same time, there would an increase in the energy of the ice cubes and an equal decrease in the energy of the boiling water, resulting in the net change of energy to be zero. However, it is important to note that no system can be perfectly closed, and there would be negligible leakage of energy to the surroundings form the thermos flask as it is not perfectly insulated.		::Although energy transfers between the system and surroundings exist, the amount of energy inflow is equal to the amount of energy outflow, and therefore the net change in energy is equal to zero. An example of a closed system could be a thermos flask. If ice cubes and boiling water are placed into the thermos at the same time, there would an increase in the energy of the ice cubes and an equal decrease in the energy of the boiling water, resulting in the net change of energy to be zero. However, it is important to note that no system can be perfectly closed, and there would be negligible leakage of energy to the surroundings form the thermos flask as it is not perfectly insulated.

Laurence12799: /* Industrial Engineering */

2019-07-28T23:27:03Z

Industrial Engineering

← Older revision		Revision as of 19:27, 28 July 2019
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	====Industrial Engineering====		====Industrial Engineering====

	:While this page refers mainly to thermodynamic and energy systems, I believe the concept of systems is essential to ~~industrial engineers~~. Industrial Engineers work on making systems as efficient as possible by minimizing waste in the production process. They also merge people, machinery, information and energy to create a product or a service. People, machinery, information and energy can be considered a system. It is an industrial engineers job to figure out the most optimal way to merge parts of the system together in order to have the greatest impact or outflow from the system to the surroundings (consumers/customers). Industrial engineers work with open systems and strive towards having a net positive outflow (i.e the resources supplied produce greater output or value).		:While this page refers mainly to thermodynamic and energy systems, I believe the concept of systems is essential to Industrial Engineers. Industrial Engineers work on making systems as efficient as possible by minimizing waste in the production process. They also merge people, machinery, information and energy to create a product or a service. People, machinery, information and energy can be considered a system. It is an industrial engineers job to figure out the most optimal way to merge parts of the system together in order to have the greatest impact or outflow from the system to the surroundings (consumers/customers). Industrial engineers work with open systems and strive towards having a net positive outflow (i.e the resources supplied produce greater output or value).

	==History==		==History==

Laurence12799 at 15:30, 26 July 2019

2019-07-26T15:30:22Z

@@ Line 401: / Line 401: @@
 ==References==
 :[https://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes| MSU Open Source for Students]
 :Matter and Interactions 4th Edition