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

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To prove (∂U/∂V)P = TCV/V for a perfect gas, begin with the internal energy equation, U, expressed in terms of temperature and volume. The discussion suggests using the differential form dU = CvdT, which relates changes in internal energy to temperature changes at constant volume. Expanding U in terms of temperature and volume will clarify the relationship, leading to the desired equation. It is emphasized to remember that this involves a partial derivative and to conclude with QED. This approach provides a structured method to derive the required proof.
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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
 
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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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