Why Can Energy and Volume Changes Be Considered Separately in Thermodynamics?

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Discussion Overview

The discussion centers around the thermodynamic equation dU = TdS - P dV and the reasoning behind considering energy and volume changes separately during a thermodynamic process. Participants explore the implications of this separation in the context of reversible and quasi-static processes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the validity of separating energy and volume changes, seeking clarification on why energy can be assumed to change before volume in the context of infinitesimal changes.
  • Another participant suggests that the process can be viewed as transitioning from an initial state to a final state through various paths, emphasizing that the equation holds as long as the process is reversible.
  • A participant raises a question about the applicability of the assumption for gases, specifically whether it only holds for quasi-static expansions.
  • Reversibility is discussed as a complex concept, with one participant noting that while a quasi-static process may not be reversible, a reversible process must be quasi-static due to the need to track all previous states.
  • Another participant defines a reversible process in terms of control over heat exchange and conservative forces, using friction as an example of a non-reversible process.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the assumptions of separability in energy and volume changes, with differing views on the implications of reversibility and quasi-static processes. No consensus is reached on the clarity of these concepts.

Contextual Notes

Participants highlight limitations in understanding the definitions of reversibility and quasi-static processes, as well as the implications of these concepts on the application of the thermodynamic equation.

aaaa202
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dU = TdS - P dV

Is in my book derived by viewing a proces of changing volume and energy in two separate steps. First you add energy with volume fixed, then change the volume.
I'm just not sure that I understand why, you are allowed to do this. I know the changes are infinitesimal but why is it, that you are allowed to assume that the energy first changes, and then after that has happened the volume changes..
 
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aaaa202 said:
dU = TdS - P dV

Is in my book derived by viewing a proces of changing volume and energy in two separate steps. First you add energy with volume fixed, then change the volume.
I'm just not sure that I understand why, you are allowed to do this. I know the changes are infinitesimal but why is it, that you are allowed to assume that the energy first changes, and then after that has happened the volume changes..

You can view it that way, but you don't have to. You have an initial state and a final state that's very close to the initial state. You can jump from the initial to the final in one little step, two little steps (as above), three little steps, even a big loop that takes you far away from the initial state and then back to the final state. That's what the law is saying - if you start at the initial state and wind up at the final state (that is very close to the initial state), it doesn't matter what steps you took to get there, that equation will hold. (as long as you do it reversibly).
 
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so for a gas that assumption would only hold, if it expands quasistatically?
I'm not quite sure what you mean by reversible to be honest.
 
Reversibility is a tricky concept. A quasi-static process may not be reversible, but a reversible process must be quasi-static because you must be able to track every previous state you had to access in order to get to the desired one.

A process is reversible if you can control the heat your system exchanges with the exterior, that is, all forces in your system must be conservative. Therefore if you push a block which has friction with the ground, this process is not reversible because you cannot take the heat generated by friction and insert back in your block for it to "push itself".
 

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