Past exam of the physics B course of the University of Cambridge / 2018 / Paper 2 / Section C / C10 / a

Write ${\gamma }^{\prime }=d\gamma /dT<0$. The Maxwell relation givesThus isothermal stretching increases the entropy. For an infinitesimal increase, $dS=-{\gamma }^{\prime }dA$; if the derivative is independent of area, this integrates to $\Delta S=-{\gamma }^{\prime }\Delta A$ 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.