= Solution
Substitute the <entropy> differential into the fundamental relation:
$$
dU=T\left(\frac{C_A}{T}\,dT-\gamma'\,dA\right)+\gamma\,dA.
$$
Therefore
$$
\boxed{dU=C_A\,dT+\left(\gamma-T\frac{d\gamma}{dT}\right)dA.}
$$
The 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 $-T\gamma'$ is the <heat> absorbed per added <area> in a reversible isothermal stretch. Both $\gamma$ and $T\gamma'$ have units $\mathrm{J\,m^{-2}}=\mathrm{N\,m^{-1}}$.
Back to article page
