Understanding Maxwell Relations: A Guide to Deriving (∂U/∂P)V=-T(∂V/∂T)S

In summary, the conversation is about deriving the equation (∂U/∂P)V=-T(∂V/∂T)S and the use of dU=TdS-PdV. The speaker is struggling with derivations and has checked various sources for help. They mention using the Thermodynamic Square and finding Maxwell relations, but are still having difficulty. They ask for help and someone suggests finding a Maxwell relation for the right-hand side. The speaker later confirms that they have solved the problem and the conversation can be closed.
  • #1
AAiden
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1. Derive (∂U/∂P)V=-T(∂V/∂T)S

2. I must use dU=TdS-PdV

3. Derivations are my weakest part of math. I checked many wikis about Total differentials, partial derivatives, Maxwell relations and derivations. I can use the Thermodynamic Square, I know how to find different Maxwell relations but I am running in circles trying to derive this equation. Thanks to anyone who can help me out!

(I am stale on my partial derivatives memory and I am failing to see how these potentials relate with these constants)
 
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  • #2
Can you find a Maxwell relation for the right-hand side?
 
  • #3
Yes, I already solved this problem, thanks.

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1. What is a Maxwell Relation?

A Maxwell relation is a mathematical equation that relates thermodynamic properties of a system that are measured at different states. It is derived from the fundamental equations of thermodynamics and can be used to calculate one property of a system using the known values of other properties.

2. Why is it important to derive a Maxwell Relation?

Deriving a Maxwell relation can help us understand the relationships between different thermodynamic properties of a system. It can also allow us to calculate one property of a system using the known values of other properties, which is useful in many practical applications.

3. How is a Maxwell Relation derived?

A Maxwell relation is derived by manipulating the fundamental equations of thermodynamics using mathematical operations such as partial derivatives and substitutions. This process involves carefully considering the variables and their relationships in the system.

4. What are some real-world applications of Maxwell Relations?

Maxwell relations are used in various fields, including chemistry, physics, and engineering. They can be applied to calculate thermodynamic properties of gases and liquids, as well as in the design and optimization of heat engines and other energy systems.

5. Are there any limitations to using Maxwell Relations?

While Maxwell relations can be incredibly useful in understanding and predicting thermodynamic properties, they have limitations. These include assumptions made about the system, such as it being in equilibrium and having well-defined properties, as well as the accuracy of the experimental data used in the calculations.

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