JEE Physics 2023 Question with Solution

Given: A cyclic process is shown on a $P-V$ diagram.

Find: The total work done in one complete cycle.

In a cyclic process, the net work done by the system is equal to the area enclosed by the loop on the $P-V$ diagram.

From the diagram, the cycle is a triangle with vertices approximately at $C(2,100)$, $D(2,400)$ and $E(4,100)$, where pressure is in $\text{Pa}$ and volume is in $\text{m}^3$.

So,

$$\Delta V = 4 - 2 = 2 \, \text{m}^3$$

and

$$\Delta P = 400 - 100 = 300 \, \text{Pa}$$

Therefore, area enclosed

$$W = \frac{1}{2} \times \Delta V \times \Delta P$$ $$W = \frac{1}{2} \times 2 \times 300 = 300 \, \text{J}$$

Since the cycle is clockwise, the work done by the system is positive.

Therefore, the correct option is D and the total work done is $300\,\text{J}$.