Question

If $W_1$, $W_2$ & $W_3$ are magnitude of work done of an ideal gas in an isothermal, adiabatic & isobaric reversible expansion process from same initial state to same final volume (only). Then, correct order will be :

• A. $W_3 > W_1 > W_2$
• B. $W_3 > W_2 > W_1$
• C. $W_2 > W_1 > W_3$
• D. $W_1 > W_2 > W_3$

Answer 1

Answer: (A)

$W_3 > W_1 > W_2$

Answer 2

Work done in a reversible expansion is the area under the P-V curve. For expansion from the same initial state to the same final volume:

1. Isobaric (constant P): Pressure remains highest ($P_1$). Area under curve is largest. ($W_3$)
2. Isothermal (constant T): Pressure decreases ($P \propto 1/V$). Curve is below isobaric. Area is smaller than isobaric. ($W_1$)
3. Adiabatic (no heat): Pressure decreases more steeply ($P \propto 1/V^\gamma$, $\gamma > 1$) due to temperature drop. Curve is below isothermal. Area is smallest. ($W_2$)

Thus, $W_3 > W_1 > W_2$.