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# The equation of a state of gas is given by $PV = nRT + Pb$. If the gas is isothermally expanded from a volume $V$ to $2V$, what is the work done during the process?

(A) $nRT \log \frac{2Vb}{V-b}$ (B) $nRT \log \frac{V-b}{2V-b}$ (C) $nRT \log \frac{2V-b}{V-b}$ (D) $nRT \log \frac{2V}{V-b}$

The equation of a state of gas is given by $PV = nRT + Pb \rightarrow P (V-b) = nRT$
In an isothermal reaction, $P (V-b) = nRT =$ constant.
Therefore, work done $= \int_{2V}^{V} PdV = \int_{2V}^{V} \large\frac{nRT}{V-b}$ $dV = nRT\log \large\frac{2V-b}{V-b}$