Thermal Phys: Show (du/dP)|t = Pkv - (cp - cv)K/B

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In summary, the conversation discussed the proof in thermal physics that is causing confusion. The task is to show that (du/dP)|t is equal to Pkv - (cp - cv)K/B for the given problem. The equations B and k were also mentioned, along with the attempt at a solution using the first law of thermodynamics. However, the speaker is currently stuck and unsure of how to proceed in proving this for the general case. They also asked if the definitions of C_P and C_V are known.
  • #1
StarTiger
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For some reason this proof in thermal is tripping me up.

Homework Statement



Show that (du/dP)|t = Pkv - (cp - cv)K/B (problem 4-4 in Carter or 1.14 in Cheng)

Homework Equations



B = 1/v(R/P) = 1/T
k= -1/v(-RT/p^2) = 1/P

The Attempt at a Solution



Start with 1st law dq=(du + Pdv) and substitute...eventually:
Get to du/dP|T dP - (du/dt)|p dt - PBvdT +PkvdP
Divide by dP

Now is where I'm stuck...
 
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  • #2
You want to prove this generally, not just for the case of the ideal gas. Do you know the definitions of and ?
 
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