Question about Maxwell equation in thermal physics

In summary, the conversation discusses how to solve for the expression of dS in terms of dT and dP. The solution involves using Maxwell's equations and the equation given in the question, and then substituting one into the other. It is determined that the expression should be purely from mathematics, and the final expression is obtained as (∂H/∂P)T = -T(∂V/∂T)P + V.
  • #1
Clara Chung
304
14

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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  • #2
What is the expression for dS interns of dT and dP?
 
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  • #3
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?
 
  • #4
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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  • #5
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!
 

1. What are Maxwell's equations in thermal physics?

Maxwell's equations in thermal physics are a set of four fundamental equations that describe the behavior of electric and magnetic fields in the presence of thermal effects, such as temperature and heat. These equations were developed by James Clerk Maxwell in the 19th century and are widely used in the study of thermodynamics and electromagnetism.

2. How are Maxwell's equations applied in thermal physics?

Maxwell's equations are used to study the behavior of electric and magnetic fields in thermal systems. They are applied to analyze the flow of heat and its interaction with electric and magnetic fields. These equations are also used to understand the behavior of materials in thermal equilibrium and to study the propagation of electromagnetic waves in thermal media.

3. What is the role of Maxwell's equations in the study of thermodynamics?

Maxwell's equations are essential in the study of thermodynamics as they provide a link between the concepts of temperature and heat with electric and magnetic fields. These equations help us understand how thermal energy is transferred and converted into other forms of energy, such as electrical or mechanical energy.

4. How do Maxwell's equations relate to the laws of thermodynamics?

Maxwell's equations are consistent with the laws of thermodynamics, which govern the behavior of energy in thermal systems. These equations provide a mathematical framework for understanding the fundamental principles of thermodynamics, such as the conservation of energy and the increase of entropy in a closed system.

5. Can Maxwell's equations be used to predict thermal behavior?

Yes, Maxwell's equations can be used to predict the thermal behavior of systems. By solving these equations, we can determine how electric and magnetic fields will interact with thermal effects, such as temperature and heat, and make predictions about the behavior of these systems. However, these predictions are limited to idealized systems, and real-world systems may exhibit more complex behavior that cannot be fully predicted by Maxwell's equations alone.

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