Project ForgeThermodynamics
Entropy & Second Law
GATE 2021
Hard
The fundamental thermodynamic relation for a rubber band is dU = TdS + τdL, where T is absolute temperature, S is entropy, τ is tension in the rubber band, and L is length. Which one of the following relations is CORRECT?
- Aτ = (∂U/∂S)_L
- (∂T/∂L)_S = (∂τ/∂S)_L
- C(∂T/∂S)_L = (∂τ/∂L)_S
- DT = (∂U/∂S)_τ
Explanation
Since dU = TdS + τdL is exact, mixed partial derivatives of U(S,L) must agree: ∂²U/∂S∂L = (∂T/∂L)_S = (∂τ/∂S)_L. This is the Maxwell relation analogous to the standard dU=TdS-pdV case.
Source: GATE ME 2021 Session 1 (ME-1) (2021)
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