The work done during the reversible isothermal expansion of one mole of hydrogen gas at $25^{\circ }\text{C}$ from a pressure of $20$ atmosphere to $10$ atmosphere is: (Given $R=2.0{\text{calK}}^{-1}{\text{mol}}^{-1}$)

Solution & Explanation

\textbf{Answer:} (A) $-413.14\text{calories}$ \textbf{Solution:} For reversible isothermal expansion, $w=-2.303nRT\log \left(\frac{P_1}{P_2}\right)$. With $n=1$, $R=2.0{\text{calK}}^{-1}{\text{mol}}^{-1}$, $T=298\text{K}$, and $\frac{P_1}{P_2}=\frac{20}{10}=2$: $w=-2.303\times 1\times 2.0\times 298\times \log 2=-2.303\times 2\times 298\times 0.3010\approx -413.14\text{cal}$. The negative sign indicates work is done by the gas on expansion. Mapped: source lowercase answer 'a' → option A.