A fluid consisting of a single component is contained in two containers at different temperatures. Show that the difference in pressure between the two containers is given by

\[\frac{\mathrm{d} p}{\mathrm{~d} T}=\frac{h-u^{*}}{v T}\]

where \(h=\) specific enthalpy of the fluid at temperature \(T\);
\(u^{*}=\) the energy transported when there is no heat flow through thermal conduction;
\(v=\) specific volume; and \(T=\) temperature.