Question

The equation of a state of a gas is given by $P(V-b)=nRT$. If $1mole$ of a gas is isothermally expanded from volume $V$ and $2V$, the work done during the process is

• A. $RT\ln \left|\frac{2V-b}{V-b}\right|$
• B. $RT\ln \left|\frac{V-b}{V}\right|$
• C. $RT\ln \left|\frac{V-b}{2V-b}\right|$
• D. $RT\ln \left|\frac{V}{V-b}\right|$

Answer 1

The correct option is A $RT\ln \left|\frac{2V-b}{V-b}\right|$

Work done is given by:
$w=\int PdV$
$w=\int nRT\frac{1}{V-b}dV=\int RT\frac{1}{V-b}dV$

$w=RT\ln \frac{V_2-b}{V_1-b}=RT\ln \frac{2V-b}{V-b}$
Hence option A is the correct answer.