Maxwell Relation Hard
Hardphysics
One Maxwell relation from fundamental thermodynamic potential U(S,V) is:
Select the correct option:
Solution
Incorrect! Answer:
(∂T/∂V)S=−(∂P/∂S)V
Maxwell relations are derived from the fact that thermodynamic potentials (like U) are state functions with exact differentials.
- From the first law: dU=TdS−PdV.
- Since dU is an exact differential, the mixed partial derivatives must be equal: (∂V∂T)S=(∂S∂(−P))V=−(∂S∂P)V This identifies a deep connection between the temperature-volume relationship and the pressure-entropy relationship.
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About This Question
- Subject
- physics
- Chapter
- thermodynamics
- Topic
- maxwell relation hard
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
(∂T/∂V)S=−(∂P/∂S)V
Maxwell relations are derived from the fact that thermodynamic potentials (like U) are state functions with exact differentials.
- From the first law: dU=TdS−PdV.
- Since dU is an exact differential, the mixed partial derivatives must be equal: (∂V∂T)S=(∂S∂(−P))V=−(∂S∂P)V This identifies a deep connection between the temperature-volume relationship and the pressure-entropy relationship.
This hard difficulty physics question is from the chapter thermodynamics, covering the topic of maxwell relation hard. It appeared in the 2025 exam.
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