A closed system undergoes a change of state by process $1 \to 2$ for which $Q_{12} = 10 J$ and $W_{12} = - 5 J$ . The system is now returned to its initial state by a different path $2 \to 1$ for which $Q_{21}$ is $- 3 J$ . The work done by the gas in the process $2 \to 1$ is:

8 J

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z e r o

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- 2 J

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+ 12 J

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Solution

The correct option is C $+ 12 J$
According to the question,
$△ Q_{1} = △ U + W_{1}$
$\Rightarrow 10 = U_{2} - U_{1} + (- 5)$
$\Rightarrow U_{2} - U_{1} = 15 J$

$△ Q_{2} = △ U + W_{2}$
$\Rightarrow - 3 = U_{1} - U_{2} + W_{2}$
$\Rightarrow - 3 = - 15 + W_{2}$
$W_{2} = 12 J$

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