Why there isn't a work term in entropy balance equation?

In summary, entropy does not have a concrete physical meaning but is associated with disorder or randomness. It represents the energy that is unable to do work. It is a mathematical derivation used to create a balance equation without a work term, based on the one directional flow of heat. This is because doing work on a system does not affect the number of compatible microstates and therefore does not transfer any entropy.
  • #1
alpyurtsever
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Homework Statement



Hi, I need your help in my homework. My Instructor asked that question? Why there is not a work term in entropy balance equation?


Homework Equations



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The Attempt at a Solution



I have researched about it and I found that,

entropy has not an exact physical meaning, however it is associated with disorder or randomness. In another point of view, entropy defines the energy which is unable to do work.
however I am not sure that these definitions are enough.

On the other hand, I think entropy is a mathematical derivation, which is done by a purpose of having a balance equation which does not involve a work term.
They have originated it from the one directional flow of heat (from high temperature to low). Is it true?

Thanks for your help
 
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  • #2
One way of looking at it is that doing work on a system changes the levels of its energy states, while transferring heat to a system changes the population of states. Entropy is quantified by the number of possible microstates (e.g., atomic arrangements) that are compatible with our macrostate observation (of pressure, for example). Since changing energy levels en masse doesn't affect the number of compatible microstates, doing (reversible) work on a system doesn't transfer any entropy, and the entropy rate in the equation above doesn't depend on work.
 

1. Why is a work term not included in the entropy balance equation?

The work term is not included in the entropy balance equation because it is already accounted for in the energy balance equation. Entropy is a measure of the disorder or randomness in a system, and work involves energy transfer and can change the disorder in a system. Therefore, including a work term in the entropy balance equation would result in double-counting the effects of work on the system's entropy.

2. Can the work term be added to the entropy balance equation?

Technically, the work term can be added to the entropy balance equation, but it would not change the overall result. As mentioned before, the work term is already accounted for in the energy balance equation, so including it in the entropy balance equation would not provide any additional information or change the final result.

3. How does neglecting the work term affect the accuracy of the entropy balance equation?

Neglecting the work term does not significantly affect the accuracy of the entropy balance equation. The work term is often much smaller than the other terms in the entropy balance equation, so neglecting it does not have a significant impact on the overall result. However, for more precise calculations, the work term should be included.

4. Is the work term always negligible in the entropy balance equation?

No, the work term is not always negligible in the entropy balance equation. In some cases, such as in systems with high levels of compression or expansion, the work term can have a significant impact on the system's entropy. In these cases, it is important to include the work term in the entropy balance equation for more accurate results.

5. Are there any exceptions where the work term is included in the entropy balance equation?

Yes, there are exceptions where the work term is included in the entropy balance equation. One example is in systems with non-conservative forces, such as friction or viscous forces, where work is done to overcome these forces and can affect the system's entropy. In these cases, the work term should be included in the entropy balance equation to accurately account for these non-conservative forces.

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