Question

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

• A. $300Rlo{g}_{10}2$
• B. $81Rlo{g}_{e}2$
• C. $900Rlo{g}_{10}2$
• D. $2.3\times 900Rlo{g}_{10}2$

Answer 1

The correct option is D $2.3\times 900Rlo{g}_{10}2$

$W=\mu RTlo{g}_e\frac{V_2}{V_1}$
$=\left(\frac{m}{M}\right)RTlo{g}_e\frac{V_2}{V_1}=2.3\times \frac{m}{M}RTlo{g}_{10}\frac{V_2}{V_1}$
$=2.3\times \frac{96}{32}R(273+27)lo{g}_{10}\frac{140}{70}=2.3\times 900Rlo{g}_{10}2$