Calculate the molar volume of methane at (672 mathrm{~K}) and 12 bar using the following methods: (a)

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Calculate the molar volume of methane at \(672 \mathrm{~K}\) and 12 bar using the following methods:

(a) Ideal gas equation of state

(b) Van der Waals equation of state, where \(a=0.2303 \mathrm{Nm}^{4} / \mathrm{mol}^{2}\) and \(b=4.3073 .12\) \(\times 10^{-5}\)

(c) Virial equation of state

(d) Virial equation of state

\[ Z=1+\frac{B}{V} \]

\[ Z=1+\frac{B P}{R T} \]

(e) Redlich-Kwong equation of state. For methane, \(T_{\mathrm{C}}=190.6 \mathrm{~K}, P_{\mathrm{C}}=45.99 \mathrm{bar}\), \(V_{\mathrm{C}}=98.6 \mathrm{~cm}^{3} / \mathrm{mol}\), and \(Z_{\mathrm{C}}=0.286\).

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