Q. One mole of $O_{2}$ gas having a volume equal to $22.4\ litres$ at $0℃$ and 1 atmospheric pressure in compressed isothermally so that its volume reduces to $11.2\ litres$. The work done in this process is
A) $1672.5\ J$
B) $1728\ J$
C) $- 1728\ J$
D) $- 1572.5\ J$
Explanation
(d) $W = - \mu RT\log_{e}{\frac{V_{2}}{V_{1}} = - 1 \times 8.31 \times (273 + 0)\log_{e}\left( \frac{22.4}{11.2} \right)}$
$= - 8.31 \times 273 \times \log_{e}{2 = - 1572.5J\ \lbrack\because\log_{e}{2 = 0.693\rbrack}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.