Blundell Thermal Physics · Problem 17.4

Rods, bubbles, and magnets

Physics — Statistical Mechanics · surface-tension-internal-energy

Problem

The entropy

S

of a surface can be written as a function of its area

A

and temperature

T

. Hence show that

\mathrm{d}U = T\,\mathrm{d}S + \gamma\,\mathrm{d}A = C_A\,\mathrm{d}T + \left[\gamma - T\left(\frac{\partial \gamma}{\partial T}\right)_A\right]\mathrm{d}A.