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Is it possible to build a jet engine that utilises excess heat for thrust or does not produce any excess heat hence no need for cooling which is wasted energy

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    $\begingroup$ You cannae change the laws of physics. $\endgroup$ – GdD Jan 11 '18 at 13:23
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No, any thermal machine always transfers energy from the heater to the cooler (Carnot cycle). The maximal yield depends on the temperature difference and cannot achieve exactly 100%. It is equal

$$ 1-\frac{T_\text{C}}{T_\text{H}} $$

where Tc is the temperature of the surrounding air and Th is the temperature of the burning fuel. Jet engine as normally understood in aviation is a thermal machine.

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