Help with a thermo derivation?

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The discussion focuses on a thermodynamics equation from a textbook, specifically how to derive a more concise expression for the partial derivative of enthalpy with respect to pressure. The original equation involves the terms of volume and temperature, and the user is confused about the substitution involving the compressibility factor (Z). They find clarity by using a different approach, calculating the change in enthalpy through internal energy and pressure. The user expresses satisfaction with their alternative method and requests for the post to be deleted, indicating they resolved their confusion. This highlights the importance of understanding thermodynamic relationships and the use of different methods for problem-solving.
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Hi all, first post so I hope this is ok to go here. It's not a homework question, just something in my book I don't get...

I am looking through my thermodynamics textbook (Smith,Van Ness, and Abbot, Intro to Chemical Eng thermodynamics) and they give the eq (6.19):

(\partialH/\partialP)T = V - T(\partialV/\partialT)P

then, "because V = ZRT/P we can write more concisely:

(\partialH/\partialP)T = -RT2/P ((\partialZ/\partialT)P)

Can anyone explain to me how they did that? I'm sure there is just some simple substitution I am missing
 
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Nevermind, I went about it by dH/dP = d(U+PV)/dP and it worked out. If an admin can delete this, that would be great.
 

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