Why are heat pumps more efficient?
Power is power right?! so why is a heat pump more 'efficient' than an element heater?
Lets assuming the heater has an air temperature sensor and a fan and that it has an electronic controller to eliminate switching losses.
Heat pumps work on a completely different principle to an element heater.
An electric heater is one of the few things which is effectively 100% efficient - that is, it converts all the incoming electrical energy into heat. A heat pump can literally pump (move and 'concentrate') heat energy from a nearby air space. It can pump (potentially four times) more heat-energy as it used electrical energy to do the pumping. You also get back the electrical energy that was turned into heat as you did the pumping.
You might therefore get '500%' efficiency of useful heat out compared to electrical energy in.
Exactly how much more energy it pumps depends on the technology and the temperature difference - the bigger the temperature difference the harder the pump has to work and the less efficient it becomes. As you pump the heat out of the outside air, the air outside becomes colder.