Q. Two moles of an ideal monoatomic gas at $27℃$ occiupies a volume of $V$. If the gas is expanded adiabatially to the volume 2$V$, then the work done by the gas will be $(\gamma = \frac{5}{3},\ R = 8.31\ J/mol - K)$
A) -2767.23 J
B) 2767.23 J
C) 2500 J
D) -2500 J
Explanation
(b) Work done $W = \frac{nR\left( T_{1} - T_{2} \right)}{\gamma - 1}$
$= \frac{nRT_{1}}{(\gamma - 1)}\left\lbrack 1 - \frac{T_{2}}{T_{1}} \right\rbrack$
$= \frac{nRT_{1}}{(\gamma - 1)}\left\lbrack 1 - \left\lbrack \frac{V_{1}}{V_{2}} \right\rbrack^{\gamma - 1} \right\rbrack$
$= \frac{2 \times 8.3 \times 300}{\left\lbrack \frac{5}{3} - 1 \right\rbrack}\left\lbrack 1 - \left( \frac{1}{2} \right)^{\frac{5}{3} - 1} \right\rbrack$
=+2767.23 J
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.