Question

A gas is taken through the cycle $ A \to B \to C \to A $, as shown in the figure. What is the net work done by the gas?

• A. 2000 J
• B. 1000 J
• C. Zero
• D. -2000 J

Hint:

To calculate the net work done by a gas in a cyclic process, find the area enclosed by the cycle on the PV diagram. The area represents the work done by the gas.

Answer 1

The Correct Option is B

The work done by the gas during a cycle is given by the area enclosed by the cycle on the PV diagram. 
The cycle consists of three parts: from A to B, from B to C, and from C to A. - From \( A \to B \), the volume increases while the pressure remains constant, so the work done is: \[ W_{AB} = P \Delta V = 3 \times 10^5 \, \text{Pa} \times (4 - 2) \times 10^{-3} \, \text{m}^3 = 600 \, \text{J} \] - From \( B \to C \), the pressure decreases while the volume increases. The work done is: \[ W_{BC} = \frac{1}{2} P \Delta V = \frac{1}{2} \times 3 \times 10^5 \, \text{Pa} \times (7 - 4) \times 10^{-3} \, \text{m}^3 = 450 \, \text{J} \] - From \( C \to A \), the pressure is constant and the volume decreases, so the work done is: \[ W_{CA} = -P \Delta V = - 3 \times 10^5 \, \text{Pa} \times (7 - 2) \times 10^{-3} \, \text{m}^3 = -1500 \, \text{J} \] The total work done is the sum of the work done in all three steps: \[ W_{\text{total}} = W_{AB} + W_{BC} + W_{CA} = 600 \, \text{J} + 450 \, \text{J} - 1500 \, \text{J} = 1000 \, \text{J} \] 
Thus, the net work done by the gas is 1000 J.