Question

Which of the following p-V curve represents maximum work done?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Work done (\(W\)) by a thermodynamic system is geometrically represented by the area under the curve in a pressure-volume (\(p-V\)) diagram.
For an expansion process, the work done is given by the integral:
\[ W = \int_{V_1}^{V_2} p \, dV \]
Step 2: Detailed Explanation:
In a \(p-V\) graph, the magnitude of work done is the area bounded by the path of the process, the volume axis (x-axis), and the vertical lines corresponding to the initial and final volumes.
1. Analysis of Graph (1): This represents a cyclic process. The net work done is only the area enclosed by the loop.
2. Analysis of Graph (2): This represents an isothermal expansion. The curve stays at a relatively higher pressure for a larger change in volume compared to others. The total shaded area under this curve is the maximum among all options.
3. Analysis of Graph (3): This shows a process where the volume change is smaller, or the pressure drops more rapidly than the isothermal case, resulting in a smaller area.
4. Analysis of Graph (4): This represents an adiabatic expansion. Since the adiabatic curve is steeper than the isothermal curve, the area under it is always less than the area under the isothermal curve for the same volume expansion.
Comparing the areas visually, graph (2) covers the largest region above the V-axis.
Step 3: Final Answer:
The maximum work done is represented by the curve in option (2).