A heat engine completes a full cycle and returns exactly to its starting state, so its internal energy is unchanged over the cycle. Using the first law with ΔU = 0, how does the source relate the net work W to the heat transfers Qh and Qc?

1. Over one complete cycle the system returns to its starting state, so ΔU = 0 for the cycle. 2. The first law states ΔU = Q - W, and the net heat transfer here is Q = Qh - Qc, the heat in from the hot reservoir minus the heat out to the cold reservoir. 3. Setting ΔU to zero gives 0 = (Qh - Qc) - W, which rearranges to W = Qh - Qc. 4. Adding the two heat transfers instead of subtracting, as in option B, would not come from setting ΔU to zero in this equation. 5. Reversing the order of subtraction, as in option C, or dividing the two quantities, as in option D, do not follow from the algebra of the first law applied to a cycle. _Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.3 Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency_