In a cyclic process ABCA for an ideal gas. In AB, BC and CA process $50 J, 20 J$ and $5 J$ heat is supplied to an ideal gas. In process AB internal energy of gas increases by $60 J$ and in process BC work done by gas is $30 J$ . The increase in internal energy of gas in process CA is :

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$55 J$

$- 50 J$

$75 J$

$50 J$

answer is B.

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Detailed Solution

From 1^st law $Q = Δ U + W$ and for any cyclic process if 1^st law is applied over entire process $Δ U = 0$ hence for complete cycle $Q = W$

Total $Q = 75$ , for $A \to B$

$50 = 60 + W_{A B}$ so $W_{A B} = - 10$

$W_{B C}$ is given $= 30$

To find $W_{C A}$

$Q = W$ so $75 = W_{A B} + W_{B C} + W_{C A}$

$75 = - 10 + 30 + W_{C A}$

Hence $W_{C A} = 55$ now applying first law for process C to A

$5 = Δ U + 55$ so $Δ U = - 50$

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