A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ______ J.

Solution

Physics sir · 4 steps

In a cycle, the net work is the area enclosed on the P-V graph, and here that area is a triangle.

1. Read the corners. The cycle is a triangle with corners at (2 m³, 100 Pa), (5 m³, 300 Pa) and (5 m³, 100 Pa). Its base runs from V = 2 to V = 5, so it is 3 m³. Its height runs from P = 100 to P = 300, so it is 200 Pa.
2. Check the sign. The gas expands along the upper slanted line and is compressed along the lower line at 100 Pa. The loop therefore runs clockwise, so the net work done by the system is positive.

   W = 1/2 × (5-2) m³ × (300-100) Pa = 1/2 × 3 × 200 = 300 J

3. Cross-check. The work done during expansion is the area under the slanted line, (100+300)/2 × 3 = 600 J. The work done on the gas during compression is 100 × 3 = 300 J. The isochoric step does no work. The net work is 600 - 300 = 300 J.
4. So. The total work done by the system in the cycle is 300 J.

The common slip: 600. Taking base times height without the factor 1/2 gives 600 J, not 300 J. The same 600 J also comes from counting only the expansion work and forgetting the work done on the gas during compression.

The idea to keep. For any cyclic process, net work equals the enclosed area on the P-V graph. A clockwise loop means positive work by the gas, and an anticlockwise loop means negative work.

Answer from the NTA final answer key. Solution by PrepWiser.