Cyclic Process

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On a pressure-volume diagram a gas is taken around a closed rectangular loop in the clockwise sense, returning exactly to its starting state. What is the net change in its internal energy over one full loop?

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Internal energy is a state function, meaning its value depends only on the current thermodynamic state and not on the path taken to reach it. In a cyclic process the gas returns to its initial state, so every state variable, including temperature and internal energy, recovers its starting value and $\Delta \cup = 0$ for the complete loop. The option equating $\Delta U$ to the enclosed area confuses internal energy with the net work done, which does equal the loop area. The option setting it equal to heat absorbed forgets that for a cycle $Q = W$ by the First Law since $\Delta \cup = 0$, so heat is not the internal energy change. The clockwise sense determines the sign of net work, not of internal energy, so that option is also wrong. The clockwise sense does matter for the work: a clockwise loop encloses positive net work done by the gas, identifying the cycle as an engine, whereas a counter-clockwise loop would represent a refrigerator. As a consistency check, applying $Q = \Delta \cup + W$ over the cycle gives $Q = W$, confirming the engine converts net absorbed heat into net work while internal energy returns precisely to where it began.

Cyclic Process

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