 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2018/paper-2/section-c/c10/a/solution

Write

γ^{'} = d γ / d T < 0

(\frac{\partial S}{\partial A})_{T} = - γ^{'} > 0.

Thus isothermal stretching increases the entropy. For an infinitesimal increase,

d S = - γ^{'} d A

; if the derivative is independent of area, this integrates to

Δ S = - γ^{'} Δ A

at fixed temperature. Mechanical energy used to create extra surface is not, in general, identical to the increase of internal energy at fixed temperature, because the stretching can also absorb heat.

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