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  4. A thermodynamic system is taken through the cycle ABCD as shown in the figure. Heat rejected by the gas during the cycle is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-xmaowo4d6trn.png />

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Q. A thermodynamic system is taken through the cycle $ABCD$ as shown in the figure. Heat rejected by the gas during the cycle is

Question

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

In a cyclic process $\Delta \text{U} = 0$ . In a cyclic process work done is equal to the area under the cycle and is positive if the cycle is clockwise and negative if anticlockwise.
Solution

$\therefore \Delta \text{W}=-\text{Area of rectangle ABCD}=-\text{P}\left(2 \text{V}\right)=-2\text{PV}$
According to the first law of thermodynamics
$\Delta \text{Q} = \Delta \text{U} + \Delta \text{W}$ or $\Delta \text{Q} = \Delta \text{W } \left(\text{As } \Delta \text{U} = 0\right)$
i.e., heat supplied to the system is equal to the work done
So heat absorbed, $\Delta \text{Q} = \Delta \text{W} = - 2 \text{PV}$
$\therefore $ Heat rejected by the gas = $2PV$