- #51

jbriggs444

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Heating 55 degree water with 60 degree ambient could theoretically generate energy. The efficiency gets so good it's actually negative :-). But that only works to get the water up to 60 degrees.I just don't see how the heat pump (heating 55F water with 60F ambient) can be more efficient than direct heating (whether it's a resistance heater or a gas flame).

Unless you are being very clever with your heat exchanger

^{(*)}, the thermodynamic efficiency depends on the ratio of the absolute temperature of the

**hot water**divided by the absolute

**ambient temperature**. If your target temperature is 150 degrees, that's ##\frac{150+459}{60+459}## which gives a ratio of 1.17. If I remember the math right, that means that 0.17 units of electrical power plus 1 unit of ambient thermal energy gives you 1.17 units of thermal energy in the hot water. That's an "efficiency" of 688%, ideally. Real world will be worse, of course.

Compare that to resistance heating with an efficiency of 100%.

In an apples to apples comparison, I think gas burners come in at around 250% -- you're not dealing with a 40% efficient natural gas powered generator and transmission system.

(*) By getting clever with the heat exchanger, I am imagining a kind of Rube Goldberg arrangement where you raise the water temperature from 55 to 60 and gain a tiny bit of energy back. Then you raise the water temperature from 60 to 65 with an outrageously high efficiency (about ten thousand percent). Then you raise it from 65 to 70 with a bit lower efficiency (about five thousand percent) and so on. You get an efficiency of 688% for the last five degrees.

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