One mole of a gas obeying the equation of state  P(V - b) =RT is made to expand from a state with coordinates $({\mathrm{P}}_1, {\mathrm{V}}_1)$ to a state with $({\mathrm{P}}_2, {\mathrm{V}}_2)$ along a process that is depicted by a straight line on a P - V diagram. Then, the work done is given by :

• A

  $\frac{1}{2}({\mathrm{P}}_1+{\mathrm{P}}_2)({\mathrm{V}}_2-{\mathrm{V}}_1)$

• B

  $\frac{1}{2}({\mathrm{P}}_2-{\mathrm{P}}_1)({\mathrm{V}}_2-{\mathrm{V}}_1)$

• C

  $\frac{1}{2}({\mathrm{P}}_1+{\mathrm{P}}_2)({\mathrm{V}}_2-{\mathrm{V}}_1+2\mathrm{b})$

• D

  $\frac{1}{2}({\mathrm{P}}_2-{\mathrm{P}}_1)({\mathrm{V}}_2+{\mathrm{V}}_1+2\mathrm{b})$