Maxwell's relations (thermodynamics): validity

In summary, the conversation includes a person who came across a slightly unusual question that asked for the conditions under which a derived maxwell relation is valid. The person mentions needing to assume certain functions of state and discusses the first law in relation to simple gas systems. They also ask for confirmation or clarification on any possible missing information. Another person responds by mentioning the mathematical fact that the order of partial differentiation does not matter for an analytic function of two variables.
  • #1
plmokn2
35
0

Homework Statement


I came across a slightly unusual question today. It started out fine, just asking me to derive a maxwell relation but then asked under what conditions is this relationship valid.

Homework Equations



The Attempt at a Solution


In deriving the relation I need to assume U, V and p are functions of state, but I can't think of any system where this wouldn't be the case. Also the first law must take the form TdS-pdV which only applies for simple gas systems without any extra freedom. But is that is?

If someone could let me know if I'm missing something obvious here (or just confirm I'm right) I'd appreciate it.
Thanks
 
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  • #2
Probably, it's the mathematical fact that the order of partial differentiation of an analytic function of two variables does not matter.

del/del x(del f/del y) = del/del y(del f/del x).
 
  • #3
Thanks
 

1. What are Maxwell's relations in thermodynamics?

Maxwell's relations are a set of equations that relate the various thermodynamic properties of a system, such as temperature, pressure, and volume, to each other.

2. Are Maxwell's relations valid for all thermodynamic systems?

Yes, Maxwell's relations are valid for all thermodynamic systems, as long as they are in a state of equilibrium.

3. How can Maxwell's relations be derived?

Maxwell's relations can be derived from the fundamental laws of thermodynamics, such as the first and second laws, and the thermodynamic potentials.

4. What is the significance of Maxwell's relations in thermodynamics?

Maxwell's relations are important in thermodynamics because they allow us to calculate the values of thermodynamic properties that are difficult to measure directly, by using properties that are easier to measure. They also help us understand the relationships between different thermodynamic properties.

5. Can Maxwell's relations be used to predict the behavior of a thermodynamic system?

Yes, Maxwell's relations can be used to predict the behavior of a thermodynamic system, as long as the system is in a state of equilibrium and the necessary thermodynamic properties are known.

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