Calculate the pressure of \(1.0 \mathrm{kmol}\) of methane occupying a volume of \(0.9 \mathrm{~m}^{3}\) in a vessel at a constant temperature of \(533 \mathrm{~K}\) by using

(a) ideal gas equation,

(b) van der Waals equation of state when \(a=0.4233 \mathrm{Nm}^{4} / \mathrm{mol}^{2}\) and \(b=3.73 \times 10^{-5} \mathrm{~m}^{3} / \mathrm{mol}\), and

(c) Redlich-Kwong equation of state when \(P_{\mathrm{C}}=123.2\) bar and \(T_{\mathrm{C}}=398 \mathrm{~K}\).