# How efficient is an electric heater?

How efficient is an electric heater?

My guess: greater than 95%. Possibly even 99%. I say this because most energy is converted into heat; some is converted into light and kinetic energy, and possibly other forms of energy.

Anyone other opinions? (This is not homework. I am just curious and I'm having a discussion with a friend who says an electric heater is horribly inefficient, less than 5%.)

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It's not a matter of opinion - so don't ask for people's opinions, ask for the answer ;-) –  David Z Dec 1 '10 at 0:02
Most of the light and kinetic energy are still absorbed by the walls, so they're still heating the room. A radiant heater heats the room primarily through light anyway, just infrared light. –  endolith Dec 2 '10 at 16:13

It depends on what you mean by efficiency.

Suppose you want to heat your house. An electric heater like you're considering would do this by converting electrical energy directly into heat. Pretty much all the electrical energy does get converted to heat, as you suggest. The energy used to get a certain amount of heat into the house is simply equal to that amount of heat. In that sense, the electric heater is 100% efficient, since energy not directly turned into heat will be turned into heat soon. That isn't a very useful way of thinking about efficiency, though, because any form of energy in your house will probably decay into heat energy pretty quickly. Your computer, television, and refrigerator are 100% efficient at heating your house from this point of view, because although they do things other than generate heat, the energy they use to do those things becomes heat in short order.

By contrast, a heat pump would heat your house by taking heat from the outside and moving it inside. The energy it needs to do this depends on the outside and inside temperatures. If the temperatures inside and outside are $T_i$ and $T_o$, an ideal heat pump (i.e. a Carnot engine) would require

$(1-\frac{T_o}{T_i})*dH$

Joules of work energy to move $dH$ Joules of heat energy from outside to inside (if the outside temperature were greater, this number is negative, meaning the heat pump can extract energy).

The efficiency of the electric heater, compared to the idealized heat pump, is

$1-\frac{T_o}{T_i}$

for given inside and outside temperatures. When the inside and outside temperatures are the same, the electric heater is zero percent efficient. If it's 0C outside and 25C inside, the electric heater is about 8% efficient.

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Very nice answer! –  Marek Nov 30 '10 at 23:34
Nice answer, but I'm thinking more of actual useful energy produced. Useful energy being heat; light, kinetic etc. all being not so useful. An electric heater may only be 8% efficient if switched on all the time, but they have thermostats for a reason. –  Thomas O Nov 30 '10 at 23:45
@Thomas I don't get what you're driving at. The kinetic energy created by an electric heater is heat - heat is the random motion of molecules. Any light created will soon become heat when it is absorbed. The 8% efficiency meant this: We want to add heat to the house. We consider two ways of doing it. One is to take heat from outside and put it in the house. To put 1 Joule of heat in the house, we will need to do .08 Joules of work. Another method is to convert electrical energy into heat. To add 1J of heat to the house with this method, we will need to use 1J of electrical energy. –  Mark Eichenlaub Nov 30 '10 at 23:58
@Thomas No, as Mark wrote, 100% of electric energy going into the heater turns into heat; light is not emitted outside, air circulation turns into heat by friction. The real question is how efficient is the whole system, with a power plant on the other side. –  mbq Dec 1 '10 at 0:02
@nibot: Heat pumps aren't very common because: A. real heat pumps are a far cry from Carnot heat engine ideals (my guess would be less than half that efficient). B. real heat pumps are extremely complicated devices (they are essentially air conditioners running in reverse). C. real heat pumps perform poorly when the temperature differential is large, and D. real heat pumps are extremely expensive (due to B) –  Billy ONeal Dec 1 '10 at 7:36

The efficiency is 100%, which is considered a poor heating efficiency. It is 100% because all light, motion, etc produced by the heater at some point becomes dissipated to heat.

Same heating efficiency have all other completely-in-door devices: heating with a TV set is as efficient as an electric heater.

However, there is a better way to heat. A typical air conditioner can heat your house by 3 joules consuming only one joule of electric energy, making it more than 300% efficient. This is done by actually cooling the outside world.

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It was a good answer Mark. Of course by drawing a lot of current some Joule heating will happen outside the house as well, in the transmission lines and transformers especially. So the efficiency will get lower depending upon where you draw the (electrical box). Some of the energy from the TV and refrigerator will also escape from the house before being degraded to heat (harmonics in the electric lines, noise, and light from the picture tube (I'd bet these loses are well under one percent)).

In any case air sourced heat pumps are far less efficient than the theoretical limit. The figure I've seen is that a quality heat pump might give you about 3.5 times as much heat as the electrical power input. Not bad compared to the alternatives, but a very long way from Carnot efficiency. Using real (im)perfect working materials is really a drag.

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I suppose the pertinent comparison is between e.g. burning fuel in a power plant, to make steam, to make electricity, which is then transmitted to a home, and then used to produce heat via a resistive heater, versus simply burning the fuel in your own home furnace. –  nibot Dec 1 '10 at 0:17