Verify the following thermodynamic relation: [begin{equation*}left(frac{partial hat{H}}{partial P} ight)_{T}=hat{V}-Tleft(frac{partial hat{V}}{partial T} ight)_{P} tag{7.48}end{equation*}]

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Verify the following thermodynamic relation:

\[\begin{equation*}\left(\frac{\partial \hat{H}}{\partial P}\right)_{T}=\hat{V}-T\left(\frac{\partial \hat{V}}{\partial T}\right)_{P} \tag{7.48}\end{equation*}\]

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