 Solution

Substitute the entropy differential into the fundamental relation:ThereforeThe coefficient of $dA$ is the change of internal energy per added area at fixed temperature, whereas $\gamma$ is the change of Helmholtz free energy per added area. Their difference $-T{\gamma }^{\prime }$ is the heat absorbed per added area in a reversible isothermal stretch. Both $\gamma$ and $T{\gamma }^{\prime }$ have units $\mathrm{J}{\mathrm{m}}^{-2}=\mathrm{N}{\mathrm{m}}^{-1}$.