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  4. Two moles of helium (γ = 5/3) expand adiabatically so that its temperature falls from 100°C to 50°C. Then the work done by the gas will be

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Q. Two moles of helium $(\gamma = 5/3)$ expand adiabatically so that its temperature falls from 100°C to 50°C. Then the work done by the gas will be

JIPMERJIPMER 2010Thermodynamics

Solution:

When a gas is expand adiabatically, work done by the gas is
$W = \frac{nR}{(\gamma - 1)} (T_1 -T_2)$
Here, $n = 2, \gamma = \frac{5}{3}$
$T_1 = 100^\circ C$ and $T_2 = 50^\circ C$
$\therefore \:\:\:\: W = \frac{2R}{\left( \frac{5}{3} - 1 \right) } (100 - 50)$
$= \frac{2R}{2/3} (50)$
$150 \, R$