Question

Which of the following graphs between pressure 'p' versus volume 'V' represents the maximum work done?

• A.
• B.
• C.
• D.

Hint:

\(W = \int P dV\). Max area \(\rightarrow\) Max work.

Answer 1

The Correct Option is D

Step 1: Concept:

Work done in a thermodynamic process is equal to the area under the pressure–volume (P–V) curve.

For a cyclic process, the work done is equal to the area enclosed by the cycle.

For a non-cyclic expansion process, the work done is equal to the area between the P–V curve and the volume axis.

Step 2: Analysis:

Graph 4 represents an expansion process from volume \(V\) to \(2V\) with pressure decreasing continuously.

The area under this curve extends over the entire region down to the volume axis, making it significantly larger than the enclosed areas in cyclic graphs.

Graphs 2 and 3 represent cyclic processes, but the areas enclosed by these cycles are comparatively smaller.

Graph 1 encloses no area, so the work done is zero.

By visual comparison, the area under the curve in Graph 4 is the largest.

Step 3: Final Answer:

The maximum work is done in Graph 4.