An ideal gas undergoes a cyclic process as shown in fig

$△ U_{B C} = - 5 k J m o l^{- 1}, q_{A B} = 2 k J m o l^{- 1}$
$W_{A B} = - 5 k J m o l^{- 1}, W_{C A} = 3 k J m o l^{- 1}$
Heat absorbed by the system during process CA is ;

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$- 18 k J m o l^{- 1}$

$+ 5 k J m o l^{- 1}$

$- 5 k J m o l^{- 1}$

$18 k J m o l^{- 1}$

answer is B.

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Detailed Solution

$△ U_{A B} = q_{A B} + W_{A B} = 2 + (- 5) = - 3 k J / m o l$

$△ U_{B C} = - 5 k J / m o l$

For cyclic process, $△ U = 0$
$△ U_{A B} + △ U_{B C} + △ U_{C A} = 0$
$△ U_{C A} = - △ U_{A B} - △ U_{B C}$
$△ U_{C A} = - (- 3) - (- 5) = 8 k J / m o l \frac{π}{6}$
$△ U_{C A} = q_{C A} + W_{C A}$
$8 = q_{C A} + 3 \Rightarrow q_{C A} = + 5 k J / m o l$
Heat absorbed has positive sign