The derivations here proceed exactly as in Problem 7.7. The singularity of these quantities arises from the last term of the two expressions, and is qualitatively similar to the singularity of the quantity \(\left(\partial C_{V} / \partial T\right)\). Note that the singularity of the combination \(\left\{\mathrm{v}\left(\partial^{2} P / \partial T^{2}\right)_{\mathrm{v}}-\left(\partial^{2} \mu / \partial T^{2}\right)_{\mathrm{v}}\right\}\) is relatively mild.