How to Prove (∂U/∂V)P = TCV/V for a Perfect Gas?

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Homework Help Overview

The discussion revolves around proving the relationship (∂U/∂V)P = TCV/V for a perfect gas, focusing on the internal energy U and its dependence on volume V under constant pressure P.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest starting with the definition of internal energy U and exploring its relationship with temperature and volume. There is mention of expanding U in terms of TC/V and considering the implications of the partial derivative.

Discussion Status

The discussion is ongoing, with participants offering different starting points and hints for approaching the problem. Some guidance has been provided regarding the use of specific equations and the importance of recognizing the nature of the derivative involved.

Contextual Notes

There is an emphasis on the need to understand the properties of ideal gases and the specific conditions under which the relationship is to be proven. Participants also note the importance of not simply copying answers and engaging with the material.

fgr
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Hi! I need to prove that:

(∂U/∂V)P = TCV/V

For a perfect gas.

But I don't know start. Can you help me please?
 
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How about starting with an equation for what U is?
 
SteamKing said:
How about starting with an equation for what U is?
Obviously, try expanding the equation of what U really is in terms of TC/V. It's a bit long, but eventually the ans becomes clear.
If ur really stuck, instead of copying an answer, try reading this-http://http://www.colby.edu/chemistry/PChem/notes/Ideal1st.pdf
 
Last edited by a moderator:
Oh, and don't forget that it's a partial derivative...and to write QED at the end. cheers :)
 
Start out with dU = CvdT for an ideal gas.

Chet
 

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