Question

The magnitude of work done by gas that undergoes a reversible expansion along the path ABC shown in the figure is

Answer 1

The reversible adiabatic expansion of the gas leads us to the conclusion that there is no energy input into the system from heating.

• Because the process is reversible, we are aware that there is no net entropy change.
• This is only possible if the pressure of the air around the expanding gas, which is expanding against all resistance, is equal to that of the surrounding air.
• The zone is an area constrained by PV Curve = $48\mathrm{J}$

Work done by the gas $=$The area under the curve

$$\begin{gathered} {\mathrm{W}}_{\mathrm{AB}}=6\times 6 \\ =36 \\ {\mathrm{W}}_{\mathrm{BC}}=\frac{1}{2}\times 4\times 6 \\ =12 \\ {\mathrm{W}}_{\mathrm{AB}}+{\mathrm{W}}_{\mathrm{BC}}=48 \end{gathered}$$

= $48\mathrm{J}$

Diagram: