Question

Two moles of an ideal gas at 2 bar and ${27}^{\circ }C$ expand isothermally against a constant pressure of 1 bar. The work done by the gas is equal to :

• A. 3.5 kJ
• B. 2.5 kJ`
• C. 1.5 kJ
• D. 4.5 kJ

Answer 1

The correct option is C 1.5 kJ

Work done in isothermal expansion-

$W=-nRT\ln \frac{P_i}{P_f}=-2.303nRT\log \left(\frac{P_i}{P_f}\right)$

Given:-

$n=2\text{moles}$

$T=27℃=(27+273)K=300K$

$P_1=2\text{bar}$

$P_2=1\text{bar}$

$R=8.314\times {10}^{-3}J$

$\therefore W=-2\times 8.314\times {10}^{-3}\times 300\times \log \left(\frac{1}{2}\right)$

$\Rightarrow W=1.5KJ$

Hence the work done by the gas is $1.5KJ$.

Hence, the correct option is $C$