Q. In an isothermal reversible expansion, if the volume of $96\ g$ of oxygen at $27℃$ is increased from $70\ litres$ to $140\ litres,$ then the work done by the gas will be
A) $300\ R\ log_{10}2$
B) $81\ R\ log_{e}2$
C) $900\ R\ log_{10}2$
D) $2.3 \times 900\ R\ log_{10}2$
Explanation
(d) $W = \mu RTlog_{e}\frac{V_{2}}{V_{1}}$
$= \left( \frac{m}{M} \right)RT\log_{e}\frac{V_{2}}{V_{1}} = 2.3 \times \frac{m}{M}RT\log_{10}\frac{V_{2}}{V_{1}}$
$= 2.3 \times \frac{96}{32}R(273 + 27)\log_{10}{\frac{140}{70} = 2.3 \times 900R\log_{10}2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.