An ideal gas undergoes the cyclic process ABCDA shown in the given $p$–$V$ diagram. What is the magnitude of the work done by the gas in one complete cycle?
(A) $6P_0V_0$
(B) $4P_0V_0$
(C) $2P_0V_0$
(D) $P_0V_0$

Question

Accepted Answer

> [!TLDR]
> Work in a cycle = area enclosed. The rectangle spans $\Delta V = 5V_0-3V_0 = 2V_0$ and $\Delta p = 4P_0-2P_0 = 2P_0$, giving $|W| = 4P_0V_0$. Answer: option (B).

The work done by a gas over a closed cycle is the area bounded by the loop in the $p$–$V$ plane:

$$|W_{	ext{cycle}}| = 	ext{area of rectangle} = \Delta p 	imes \Delta V.$$

From the diagram the rectangle has width (volume change) $\Delta V = 5V_0 - 3V_0 = 2V_0$ and height (pressure change) $\Delta p = 4P_0 - 2P_0 = 2P_0$. Therefore …

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