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The work done during reversible isothermal expansion of one mole of hydrogen gas at $25^\circ C$ from pressure of 20 atmosphere to 10 atmosphere is: (Given $R = 2.0$ cal $K^{-1}mol^{-1}$)
A
413.14 calories
B
100 calories
C
0 calorie
D
-413.14 calories
Detailed Solution
For reversible isothermal expansion: $W = -2.303\,nRT\log\frac{P_1}{P_2}$
$W = -2.303 \times 1 \times 2 \times 298 \times \log\frac{20}{10}$
$= -2.303 \times 2 \times 298 \times 0.3010$
$= -413.14$ calories