Power input smaller than output? How can this be?

I am not an electrical engineer, and I was looking at the energy ratings of air conditioners and I'm having a hard time understanding why the output in kW is greater than the power input in kW. My understanding is that power input and output should be about the same in a closed system. Is this a terminology/marketing confusion? What do these statistics mean?

Answer

I didn't follow the link, but air conditioners can move more heat than the power it takes to do the moving.

This is a case where the Carnot efficiency works in your favor. Carnot says that the maximum possible theoretical efficiency of a heat engine is Tdiff / Thot, where the temperatures are expressed in a absolute linear scale, like Kelvin. For example, if you had a reservoir of boiling water (373 K) and icewater (273 K), even a ideal heat engine can't be more than 100 K / 373 K = 27% efficient. Put another way, for a heat flow of 100 W in this setup, you can't ever extract more than 27 W of work.

However, heat pumps do the reverse. A perfect heat pump would only require 27 W of work input to move 100 W of heat from 273 K to 373 K. This is not a violation of conservation of energy because work can't be extracted from this heat without hitting the 27% limit as above.

Air conditioners are heat pumps. They move heat from the room to the outside, presumably from cooler to warmer. The temperature difference is a lot less than the difference between boiling and frozen water, so the Carnot efficiency is much less too. That is actually good news for air conditioners, because they benefit according to the reciprocal of the Carnot efficiency. Of course real air conditioners are real systems with inevitable real inefficiencies, so you can't just take the reciprocal of the Carnot efficiency to determine their power input requirements. But, this still works in their favor, and the systems are good enough for reasonable temperature differences to still require less work in than the amount of heat they move around.

For more details, look up "Carnot efficiency". Surely there is much written about it out there.