Determine the molar volume of \(n\)-butane at \(500 \mathrm{~K}\) and \(8 \mathrm{MPa}\) by making use of

(a) the ideal gas law and

(b) the virial equation of state. The virial coefficients of \(n\)-butane are given by \(B=-0.265 \times 10^{-3} \mathrm{~m}^{3} / \mathrm{mol}\) and \(C=0.3025 \times 10^{-7} \mathrm{~m}^{6} / \mathrm{mol}^{2}\).