# Air conditioners and the law of conservation of energy?

Sorry if this is a stupid question, but I have often been told that air conditioners are more efficient than an electric heater, because, the story goes, if you put say 1 kW of electricity in the electric heater, you get 1 kW worth of heat, but if you put 1 kW worth of electricity into the air conditioner, you can get 3-4 kW worth of heat (not sure about the exact numbers).

Assuming the law of conservation of energy is not broken, where do the other 3 kW worth of heat come from? I assume it should be the air outside, but the outside air is usually colder than the temperature you are trying to get, so how do you use a -5C air from the outside to raise the temperature of a room from +15C to +25C?

• The outside air is cooled further than the ambient temperature and the heat is transferred to the inside. The energy exists in the air outside and is moved to inside, while the temperature outside falls because the heat was removed. The energy spent by the compressor/ expansion cycle is used so that the energy from outside can be transferred inside. 1KW of electricity can move heat from cool outside to warm inside to make it warmer. Dec 28, 2013 at 17:47