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KingoPants t1_j0azou2 wrote

To explain this just a bit further for people who have never taken thermodynamics.

You can't take heat and turn it into useful work. You always need to raise entropy in any spontaneous process (second law of thermodynamics).

Cutting out the motivations, basically taking a (infinitely small) amount of heat energy out of a system reduces it's entropy by Q/T where Q is heat in joules and T is absolute temperature in kelvin. Adding that much heat energy also adds that much entropy.

If you have a hot and a cold reservoir with temperatures T_h and T_c then and you are taking heat Q_h out of T_h and putting heat Q_c into T_c then because the entropy change must be positive you get that Q_c/T_c > Q_h/T_h.

By energy conservation the work you get out of this process is W = Q_h - Q_c. If you do some basic algebra you can figure out that W/Q_h < (T_h - T_c) / T_h

The cool thing is the algebraic derivations for this efficiency are very easy although the verbal explaining for why entropy works like this is much more complex.

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