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  4. Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: (R is universal gas constant)

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Q. Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: $(R$ is universal gas constant)

Thermodynamics

Solution:

Given, $\Delta Q=4 \Delta W$
But, $\Delta W=\Delta U=\Delta Q$
$\therefore \Delta U=3 \Delta W=\frac{3}{4} \Delta Q$
$\Rightarrow n C_{V} \Delta T=\frac{3}{4} n C \Delta T$
or, $C=\frac{4}{3} C_{V}=\frac{4}{3}\left[\frac{3 R}{2}\right]=2 R$