Calculate the molar volume of methane at \(773 \mathrm{~K}\) and 15 bar using the following methods:

(a) Ideal gas equation of state

(b) van der Waals equation of state, with \(a=0.2303 \mathrm{Nm}^{4} / \mathrm{mol}^{2}\) and \(b=4.3073 .12 \times\) \(10^{-5} \mathrm{~m}^{3} / \mathrm{mol}\)

(c) Virial equation of state, \(Z=1+\frac{B}{V}\)

(d) Redlich-Kwong equation of state, when \(T_{\mathrm{C}}=190.6 \mathrm{~K}\) and \(P_{\mathrm{C}}=45.99\) bar.

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 \(Z_{\mathrm{C}}=0.286\).