Question about Maxwell equation in thermal physics

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Homework Help Overview

The discussion revolves around the application of Maxwell's equations in the context of thermal physics, specifically focusing on the relationships between enthalpy, entropy, temperature, and pressure. The original poster is attempting to solve a problem that involves differentiating equations and substituting variables related to thermodynamic properties.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the differentiation of thermodynamic equations and the implications of variable subscripts. Questions arise regarding the expression for entropy in terms of temperature and pressure, and whether this should be derived from the problem's context or purely from mathematical principles.

Discussion Status

Some participants have provided insights into the mathematical relationships involved, suggesting that certain expressions can be derived without relying on the specific context of the problem. There is an ongoing exploration of how to correctly apply the equations and the implications of different variable dependencies.

Contextual Notes

Participants are navigating the complexities of thermodynamic equations, including the need for clarity on variable subscripts and the appropriate expressions for entropy. The discussion reflects a mix of theoretical understanding and practical application of Maxwell's equations.

Clara Chung
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Homework Statement


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Homework Equations

The Attempt at a Solution


How to do part ii)?
I differentiate part i with respect to p
(∂H/∂P)T = T (∂S/∂P)T + V ...(1)
Then I used the equation given in the question,
Applying maxwell equation I got
(∂T/∂V)S = -(∂P/∂S)V ...(2)
I planned to substitute (2) into (1), However the subscript of
-(∂P/∂S)V is V , but the subscript of (∂S/∂P)T is T which are not the same
What should I do?
 

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What is the expression for dS interns of dT and dP?
 
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Chestermiller said:
What is the expression for dS interns of dT and dP?
Do I need the expression according to the information given by the question or from dQrev/T?
 
Clara Chung said:
Do I need the expression according to the information given by the question or from dQrev/T?
Neither. Purely from mathematics.
 
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Chestermiller said:
Neither. Purely from mathematics.
If it is purely from mathematics.. I think I can do it like this
G=H-TS
dG=dH-TdS-SdT
dG=VdP-SdT
so
(∂V/∂T)P = - (∂S/∂P)T
Now I can put it into (∂H/∂P)T = T (∂S/∂P)T + V ...(1)
So
(∂H/∂P)T = -T(∂V/∂T)P + V
Thanks for helping!
 

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