Solution to 2008 Problem 79

First solve for P in terms of V and T:
\begin{align*}P = \frac{RT}{V - b} - \frac{a}{V^2}\end{align*}
The differential work done by the gas is dW = P dV, so the total work done by the gas is
\begin{align*}\int_1^2 P dV &= \int_{V_1}^{V_2} \left(\frac{RT}{V - b} - \frac{a}{V^2} \right) dV \\&= RT\int_{V_1}^{...
Therefore, answer (D) is correct.

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