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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?

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  • $\begingroup$ 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. $\endgroup$ – anna v Dec 28 '13 at 17:47
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When using AC to cool a room, you are moving heat from inside the room to outside of it (lets say 3kW worth of heat flow), at the cost of electricity of course (1kW). The machine itself cannot be 100% efficient, meaning a portion of that 1kW cannot and did not actually do work, e.g. 0.8kW of power was used to pump that 3kW across the walls, while 0.2kW of waste heat was produced by the machine itself.

From this example it is shown that for 1kW worth of electric power, we can cause the inside of a room to lose heat at a rate of 3kW while causing the outside to gain it at 3.2kW. If we reversed the AC so that heat is being pumped into the room, we can then get 3.2kW worth of heating for 1kW worth of electric power--a coefficient of performance (COP) of 3.2. This is better than resistive heating, which gives us 1.0.

Of course, the numbers won't be as good if you just reversed the system. As you probably already guessed, it is harder to pump heat from -5'C air to +15'C air than the other direction. But it is not difficult, let alone impossible, after all, refrigerators move heat from from the freezer compartment at -5'C to kitchen air at +15'C to +25'C all the time.

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    $\begingroup$ Uhh... You're putting in electrical energy at the rate of ! kW, the inside of the room is "contributing" at a rate of 3 kW, and the outside is receiving energy at a rate of 3.2 kW. Where does the missing energy, 800 joules/sec, go? $\endgroup$ – DJohnM Dec 28 '13 at 20:54
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I am not sure I can really come up with a simple answer to this. But the key concept is something called Latent heat.This is where heat is going into say the Evaporator outside a room but notice it is very cold. You would think that heat going in would raise the temp of the evaporator, but what is happening is that a fluid is being converted into a gas, if you like "boiling" but boiling at say -30 deg C the heat going in does not raise the temp (as long as the system can keep up pumping the gas around converting to a fluid, then to a gas and so on. The heat has gone into breaking the bonds to form a gas "boiling" at say around -30 C and then when we change from gas to liquid the heat is pumped out via the condenser.

We must also realise that air for example can be very cold but still contain an enormous amount of heat. Sometimes we make the evaporator really huge in area and put it underground so that the temp in the ground or even water can be say 10C when air temp is -10C we then have an enormous heat source. So truly we can have a heat pump that can have really high Coefficient of Performance something like 12 times. Of course these heat pumps become very expensive.

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