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One mole of a gas obeying the equation of state P(V - b) =RT is made to expand from a state with coordinates $(P_{1}, V_{1})$ to a state with $(P_{2}, V_{2})$ along a process that is depicted by a straight line on a P - V diagram. Then, the work done is given by :

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$\frac{1}{2} (P_{1} + P_{2}) (V_{2} - V_{1})$

$\frac{1}{2} (P_{2} - P_{1}) (V_{2} + V_{1} + 2 b)$

$\frac{1}{2} (P_{2} - P_{1}) (V_{2} - V_{1})$

$\frac{1}{2} (P_{1} + P_{2}) (V_{2} - V_{1} + 2 b)$

answer is A.

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Detailed Solution

$P \propto V$ in the given process
P = AV + B
W = Area under line
$= \frac{1}{2} (P_{1} + P_{2}) (V_{2} - V_{1})$

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