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Empirical observations of a thermodynamic system have shown that:

$$\begin{align}C_{\mathrm m,V} &\neq C_{\mathrm m,V}(T) \\[6pt] \left(\frac{\partial U}{\partial V_\mathrm m}\right)_{T} &= f(V_\mathrm m) \\[6pt] \left(\frac{\partial U}{\partial p}\right)_{V} &= g(V_\mathrm m) \end{align}$$

where $f$ and $g$ are functions of the molar volume, $V_\mathrm m$. Determine the state equation.

How can I solve this problem?

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