Question

In an isothermal reversible expansion if the volume of $96\text{g}$ of oxygen at ${27}^{\circ }\text{C}$ is increased from $70\text{L}$ of $140\text{L}$, then the work done by the gas will be

• A. $300{\text{R log}}_{10}2$
• B. $81{\text{R log}}_{e}2$
• C. $900{\text{R log}}_{10}2$
• D. $2070{\text{R log}}_{10}2$

Answer 1

The correct option is D $2070{\text{R log}}_{10}2$

As work done in an isothermal process is given by
$W=n{\text{RT log}}_e\frac{V_2}{V_1}$
$=\left(\frac{m}{M}\right){\text{RT log}}_e\frac{V_2}{V_1}=2.3\times \frac{m}{M}{\text{RT log}}_{10}\frac{V_2}{V_1}$
$=2.3\times \frac{96}{32}R(273+27){\text{log}}_{10}\frac{140}{70}=2.3\times 900{\text{R log}}_{10}2=2070{\text{R log}}_{10}2$