Calculate the work done during the isothermal reversible expansion of a van der Waals gas. Account physically for the way in which the coefficients a and b appear in the final expression. Plot on the same graph the indicator diagrams for the isothermal reversible expansion of

(a) A perfect gas,

(b) A van der Waals gas in which a = 0 and b = 5.11 × 10⁻² dm³ mol⁻¹, and

(c) A = 4.2 dm⁶ atm mol⁻² and b = 0. The values selected exaggerate the imperfections but give rise to significant effects on the indicator diagrams. Take V_i = 1.0 dm³ , n = 1.0 mol, and T = 298 K.