The Berthelot equation of state is given by [ left(P+frac{a}{T V^{2}} ight)(V-b)=R T ] where (a) and

The Berthelot equation of state is given by

\[ \left(P+\frac{a}{T V^{2}}\right)(V-b)=R T \]

where \(a\) and \(b\) are constants. Show that \(a=\frac{27 R^{2} T_{\mathrm{C}}^{3}}{64 P_{\mathrm{C}}}, b=\frac{R T_{\mathrm{C}}}{8 P_{\mathrm{C}}}, Z_{\mathrm{C}}=\frac{3}{8}\) from the knowledge of point of inflexion at critical isotherms.