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In a practical heat engine, heat is generated by burning a fuel, work is extracted from this heat resulting in the working fluid cooling, and heat is then rejected at the lower temperature. As you must know, in an internal combustion engine heat is rejected both in the engine cooling system and the exhaust.

In a power plant, using water/steam as the working fluid in a closed cycle, there are four phases in the cycle: 1. Water is pumped at high pressure into a steam raising unit (boiler) 2. Heat from the fuel, be it coal, oil, gas, or nuclear, is added to the water causing it to become steam 3. the steam is expanded through a turbine doing work, that is driving the generator 4. the steam is condensed back to water using external cooling water. This is called the Rankine cycle. At stage 4 heat is being rejected into the external cooling water, and this heat is lost. It is minimised by running the condenser under vacuum so that steam at less than 100 celsius can still do work, and the final turbine discharge temperature is as low as 30C. Theoretically the efficiency of such a cycle is maximised by making the steam to the turbine as hot as material constraints allows, and the condenser vacuum as low as the local cooling water temperature will allow. The maximum practical efficiency of such a plant is about 42 percent, meaning that 58 percent of the heat from the fuel is rejected. For a PWR nuclear plant the steam temperature is much lower and the cycle efficiency is less, more like 30 percent.

I hope this enables you to see why in a practical heat engine there must be heat rejection. There are several entries in Wikipedia for further reading, see 'Heat Engines' first.

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Q: Why is there heat rejection in a thermodynamic process?
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