GATE ME 2021 Set 1 — Question 39
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Thermodynamics → Laws & Properties → Maxwell Relations
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Question
The fundamental thermodynamic relation for a rubber band is given by , where is the absolute temperature, is the entropy, is the tension in the rubber band, and is the length of the rubber band. Which one of the following relations is CORRECT?
Correct answer
(B) ((∂ T)/(∂ L))_S = ((∂ τ)/(∂ S))_L
Solution
Given the fundamental thermodynamic relation for a rubber band:This is an exact differential of the internal energy
and Furthermore, the condition for an exact differential is:Substituting , , , and :This is the Maxwell relation corresponding to the given fundamental equation. Therefore, option (B) is correct.
U(S, L). For any exact differential of the form , we have:Comparing this with the given relation:and Furthermore, the condition for an exact differential is:Substituting , , , and :This is the Maxwell relation corresponding to the given fundamental equation. Therefore, option (B) is correct.
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