Thermodynamic processes

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Question

An ideal gas is taken through the cycle $A \to B \to C \to A$ , as shown in Fig. If the net heat supplied to the gas in the cycle is 15 J, the work done by the gas in the process $C \to A$ is _____ J.

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Solution

$I n c o m p l e t e c y c l e, △ U = 0$
$∴ W_{A B} + W_{B C} + W_{C A} = Q_{N e t}$
$\Rightarrow 100 (2 - 1) + 0 - \frac{1}{2} (P_{C} + 100) (1) = 15$
$\Rightarrow P_{C} = 70 N m^{- 2}$
$∴$ $W_{C A} = - \frac{1}{2} (P_{C} + 100) (1) = - \frac{1}{2} (70 + 100) \times 1 = - 85 J$

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