A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

Solution

Physics sir · 3 steps

Work is the area under each path: positive while the gas expands, negative while it is compressed.

1. D to E. The gas expands from 2 m³ to 5 m³ as pressure falls linearly from 600 to 300 N m⁻². The area under this line is a trapezium, and the work is positive: W_(DE) = (600 + 300)/2 × 3 = 1350 J.
2. E to F. At constant 300 N m⁻² the volume goes back from 5 m³ to 2 m³. That is a compression, so the work is negative: W_(EF) = 300 × (2 - 5) = -900 J.

   Wₜₒₜₐₗ = 1350 J + (-900 J) = 450 J

3. So. The net work is the area of triangle DEF, 1/2 × 3 × 300 = 450 J. It is positive because the expansion happens at higher pressure than the compression. The answer is (b).

The idea to keep. On a P-V graph, take the area under each segment. Give it a plus sign if volume increases and a minus sign if volume decreases, then add the pieces.

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