An ideal gas is taken around a closed cycle ABCA on a p–V diagram. The points are A (V, p), B (3V, 4p) and C (3V, p), joined by straight lines. What is the work done during one complete cycle?

Correct answer: (d) 3pV

Explanation

In a p–V diagram, the work done in one complete cycle equals the area enclosed by the cycle.

Here A (V, p), B (3V, 4p) and C (3V, p) form a right-angled triangle:

• base (along volume) = 3V − V = 2V;
• height (along pressure) = 4p − p = 3p;
• area = ½ × 2V × 3p = 3pV.

The path A → B → C → A is clockwise in the diagram, so this net work is done by the gas.