Proof of dU=TdS-PdV: dw=PdV Not dw=PdV+vdP

  • Thread starter Thread starter asdf1
  • Start date Start date
  • Tags Tags
    Proof
Click For Summary

Homework Help Overview

The discussion revolves around the thermodynamic equation dU=TdS-PdV, specifically focusing on the differentiation of work done, questioning why dw=PdV is preferred over dw=PdV+vdP.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definitions and implications of work in thermodynamics, questioning the role of pressure and volume changes in the context of internal energy.

Discussion Status

Some participants are examining the reasoning behind the equations, with one providing a rationale related to the nature of work and internal energy. There is an ongoing exploration of the concepts without a clear consensus.

Contextual Notes

One participant notes the absence of their textbook, which may limit their ability to reference specific details or definitions during the discussion.

asdf1
Messages
734
Reaction score
0
When proving the equation,
dU=TdS-PdV

why is dw= PdV not dw= PdV +vdP?
 
Physics news on Phys.org
I think it is as you wrote, but don't quote me. I'm at school and don't have my book infront of me.
 
asdf1 said:
When proving the equation,
dU=TdS-PdV

why is dw= PdV not dw= PdV +vdP?
Work (force x distance) is done only if the pressure (force/area) acts over some change in volume (area x distance moved). If there is no change in volume, the force does not act over any distance - ie. the pressure just builds up but does not move anything (ie. it just increases internal energy). So, VdP is part of the internal energy of the gas, not the work done by the gas.

AM
 
thank you!
 

Similar threads

What is ##Tds## in this equation : ##dU = Tds - PdV##
  • · Replies 14 ·
Replies
14
Views
3K
Entropy and the Helmholtz Free Energy of a Mass-Piston System
  • · Replies 8 ·
Replies
8
Views
2K
What Happens to Kinetic Energy of the Piston in an Isothermal System?
  • · Replies 21 ·
Replies
21
Views
3K
Please prove that dW=-vdP where v is specific volume
  • · Replies 7 ·
Replies
7
Views
8K
Undergrad Gibbs Free Energy Correction Term
  • · Replies 5 ·
Replies
5
Views
2K
Chemistry How to derive 2nd law extremum principles for U, A, G, and H?
  • · Replies 1 ·
Replies
1
Views
3K
Heat Capacity relations for 1st order phase transition
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Reversible / Irreversible Fundamental Equation
  • · Replies 3 ·
Replies
3
Views
2K
Chemistry What does the differential of U mean in an irreversible process?
  • · Replies 11 ·
Replies
11
Views
2K
How can I demonstrate that the integral of vdP is used to calculate work in flow machines?
  • · Replies 6 ·
Replies
6
Views
2K