Help with a thermo derivation?

In summary, the conversation is about a question regarding a thermodynamics textbook and a specific equation (6.19) in the book. The person is confused about how the equation was simplified and is asking for an explanation. However, they later figure it out themselves and ask for the post to be deleted.
  • #1
allover
2
0
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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  • #2
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.
 

1. What is thermo derivation?

Thermo derivation is a mathematical process used in thermodynamics to derive equations that relate to the transfer of energy and heat between different systems.

2. Why is thermo derivation important?

Thermo derivation is important because it allows scientists and engineers to understand and predict how energy is transferred in various systems, which is crucial in many fields such as engineering, chemistry, and physics.

3. How does thermo derivation work?

Thermo derivation involves using mathematical operations, such as differentiation and integration, to manipulate existing thermodynamic equations and derive new ones that describe the behavior of a system under specific conditions.

4. What are some common applications of thermo derivation?

Thermo derivation is used in many areas, including the design of energy-efficient systems, the study of phase transitions, and the analysis of heat transfer in engines and power plants.

5. Are there any challenges associated with thermo derivation?

Yes, thermo derivation can be challenging due to the complexity of the equations involved and the need for a solid understanding of thermodynamics and mathematical concepts. It also requires careful attention to units and assumptions to ensure accurate results.

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