Question

Equation of state for a gas is given by $P(V-b)=nRT$. If 1 mole of gas is isothermally expanded from volume V to 2V, then total work done during that process is

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

Answer 1

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

Work done in any process can be given by;
$W={\int }_{V_1}^{V_2}PdV$
Where, $P=\frac{nRT}{V-b}$
$W={\int }_V^{2V}\frac{nRT}{V-b}dV=nRT{\left[ln\right(V-b\left)\right]}_V^{2V}$
$W=nRTln\left|\frac{2V-b}{V-b}\right|$