A sample of an ideal gas is taken through the cyclic process $ABCA$ as shown in figure. It absorbs, $40\,J$ of heat during the part $A B$, no heat during $BC$ and rejects $60\,J$ of heat during $CA$. $A$ work $50\,J$ is done on the gas during the part $BC$. The internal energy of the gas at $A$ is $1560\,J$. The work done by the gas during the part $CA$ is.............$J$
JEE MAIN 2022, Medium
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$\Delta Q_{\text {cycle }}=40-60=\Delta W$
$\Rightarrow \Delta W =-20 J = W _{ BC }+ W _{ CA }$
$\Rightarrow W _{ CA }=-20 J - W _{ BC }$
$=-20-(-50)$
$=30\,J$
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