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The fundamental thermodynamic relation is dU = TdS + τdL, where T is the temperature and τ is the tension in the rubber band. Which one of the following relations is correct?
- (A) τ = (∂U/∂S)L
- (B) (∂T/∂L)S = (∂τ/∂S)L
- (C) (∂T/∂S)L = (∂τ/∂L)S
- (D) T = (∂U/∂S)τ
Correct answer: (B) (∂T/∂L)S = (∂τ/∂S)L
Solution
Option B is correct because it reflects the relationship between temperature and tension in a system where entropy is held constant, demonstrating how changes in one variable affect the other under those specific conditions.
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