A real gas within a closed chamber at $27^{\circ} \mathrm{C}$ undergoes the cyclic process as shown in figure. The gas obeys $P V^3=R T$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R=8 \mathrm{~J} / \mathrm{mol} \mathrm{K}$ ):

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Aicharya · Accepted Answer

$\mathrm{W}_{\mathrm{AB}}=\int \mathrm{PdV} \quad$ (Assuming $\mathrm{T}$ to be constant) $\begin{aligned} & =\int \frac{\mathrm{RTdV}}{\mathrm{V}^3} \ & =\mathrm{RT} \int_2^4 \mathrm{~V}^{-3} \mathrm{dV} \ & =8 	imes 300 	imes\left(-\frac{1}{2}\left[\frac{1}{4^2}-\frac{1}{2^2}ight]ight) \ & =225 \mathrm{~J}\end{aligned}$ $\begin{aligned}& \mathrm{W}_{\mathrm{BC}}=\mathrm{P} \int_4^2 \mathrm{dV}=10(2-4)=-20 \mathrm{~J} \& \mathrm{~W}_{\mathrm{CA}}=0 \& 	herefore \mathrm{W}_{	ext {cycle }}=205 \mathrm{~J} \end{aligned}$

A real gas within a closed chamber at $27^{\circ} \mathrm{C}$ undergoes the cyclic process as shown in…

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