Question: 79: Which of the following \mathrm{p}-\mathrm{V} curve represents maximum work done?
Answer: Option (4)
Explanation:
The work done by a gas in a \mathrm{p}-\mathrm{V} process is equal to the area under the curve, given by W=\int p\,dV.
For a given change in volume between two fixed states, the work done depends on the path followed.
In an isothermal reversible expansion, the gas remains in equilibrium at every stage and follows a smooth hyperbolic curve described by pV=\text{constant}.
This reversible isothermal path gives the maximum possible work because the pressure at every intermediate volume is maximum compared to any irreversible process.
In option (4), the curve represents a smooth isothermal reversible expansion, which encloses the maximum area under the curve.
Vertical lines represent no change in volume, so no work is done.
Sudden drops or irregular paths represent irreversible processes,
which always give less work than the reversible process.
Therefore, the \mathrm{p}-\mathrm{V} curve
in option (4) represents maximum work done.