Question

The work done by a gas when it undergoes a state change from 1 $\to$ 2 isothermally is

• A. $nRTln\left(\frac{V_1}{V_2}\right)$
• B. $nRTln\left(\frac{V_2}{V_1}\right)$
• C. $nRT\left(\frac{V_1}{V_2}\right)$
• D. $nRT\left(\frac{V_2}{V_1}\right)$

Answer 1

The correct option is B

$nRTln\left(\frac{V_2}{V_1}\right)$

For an isothermal process T is constant.

Therefore from ideal gas equation we get -
pV = nRT

$\Rightarrow p=\frac{nRT}{V}$ ...(1)

We know that the work done in any process can be calculated using -

$W=\int pdV$ ...(2)

From (1) and (2) -

$W={\int }_{v_1}^{v_2}\frac{nRT}{V}dV$

$=nRT{\int }_{v_1}^{v_2}\frac{dV}{V}$
$W=nRTln\left(\frac{V_2}{V_1}\right).$