thermodynamics - 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%.)

Answer

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.