Help with a thermo derivation?

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SUMMARY

The discussion centers on a thermodynamic derivation from the textbook "Intro to Chemical Engineering Thermodynamics" by Smith, Van Ness, and Abbot. The equation presented, (\partialH/\partialP)T = V - T(\partialV/\partialT)P, is simplified using the ideal gas law, V = ZRT/P, leading to the expression (\partialH/\partialP)T = -RT2/P ((\partialZ/\partialT)P). The original poster resolves their confusion by utilizing the relationship dH/dP = d(U+PV)/dP, confirming the validity of the derivation.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically enthalpy and pressure relationships.
  • Familiarity with the ideal gas law and compressibility factor (Z).
  • Knowledge of partial derivatives in thermodynamics.
  • Experience with the concepts of internal energy (U) and its relation to enthalpy (H).
NEXT STEPS
  • Study the derivation of the ideal gas law and its implications in thermodynamics.
  • Learn about the compressibility factor (Z) and its role in real gas behavior.
  • Explore the application of partial derivatives in thermodynamic equations.
  • Investigate the relationship between internal energy (U) and enthalpy (H) in various thermodynamic processes.
USEFUL FOR

Students and professionals in chemical engineering, particularly those focusing on thermodynamics and fluid mechanics, will benefit from this discussion.

allover
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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):

([tex]\partial[/tex]H/[tex]\partial[/tex]P)T = V - T([tex]\partial[/tex]V/[tex]\partial[/tex]T)P

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

([tex]\partial[/tex]H/[tex]\partial[/tex]P)T = -RT2/P (([tex]\partial[/tex]Z/[tex]\partial[/tex]T)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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