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

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SUMMARY

The discussion centers on the thermodynamic equation dU = TdS - P dV, which describes changes in internal energy (dU) as a function of entropy (S) and volume (V). Participants clarify that energy and volume changes can be treated separately in a quasi-static process, allowing for a stepwise approach to understanding thermodynamic transformations. The concept of reversibility is emphasized, where a process is reversible if it can be conducted without dissipating energy, and all forces involved are conservative. This understanding is crucial for accurately applying thermodynamic principles in practical scenarios.

PREREQUISITES
  • Understanding of thermodynamic principles, particularly the first and second laws of thermodynamics.
  • Familiarity with the concepts of internal energy (U), entropy (S), and pressure (P).
  • Knowledge of quasi-static and reversible processes in thermodynamics.
  • Basic mathematical skills to manipulate differential equations in thermodynamic contexts.
NEXT STEPS
  • Study the derivation and implications of the first law of thermodynamics.
  • Learn about quasi-static processes and their significance in thermodynamic systems.
  • Explore the concept of reversibility in thermodynamics and its practical applications.
  • Investigate the role of conservative forces in thermodynamic processes.
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This discussion is beneficial for students and professionals in physics and engineering, particularly those focusing on thermodynamics, as well as researchers interested in energy systems and their efficiencies.

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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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