The $/capacity may be quite different. The capacity of burner systems is generally cheap, so you oversize them and if you need more heat, you just burn more fuel. The capacity of a heat pump is relatively expensive, so you size it up to something reasonable, and in an unusually cold day you may hit the limits of how much joules you can get out of it.
Also, the $/fuel is different - if one system gets three times more joules from the same fuel, it doesn't mean it's more efficient as the other system may be using four times cheaper fuel; so a 300%-efficient heat pump is more efficient than a resistive heater but may be less efficient than a furnace burning cheap fuel.
Capacity. Heat pumps are typically lower capacity (in BTU/hr delivered) than a fuel burning appliance and that capacity drops with very cold outside temps.
The trick here is that with heat pumps, they aren't generating the heat, just moving it. As such, you can have, e.g. a 1 kW heat pump moving much more than 1 kW of heat. Wheras with a resistive heater, the best you can do is turn 1 kW of electric power into 1 kW of heat output.
A heat pump operates at 2x to 4x the power efficiency as compared to resistive heating. Many places are unfortunately only doing resistive heating because of cheap install cost. If we can replace that with a heat pump that's a big win for everyone.
This is an interesting example of how there is a difference betweena policy being a "heat pump" and a "resistive heater", and that both can occur simultaneously.
The problem with "heat pumps" is that they necessitate a "cold" side, from which they "pump the heat" to the "hot" side. Their goal isn't to increase the overall "heat" in the system, it's to move the "hot" all to one side.
A "resistive heater" can add "heat" to the system more evenly, but is less efficient and you won't see "temperatures" rise nearly as quickly.
> Heat pumps are 3-4 times as energy efficient as a gas furnace.
This depends totally on the outside temperature. Larger, more expensive heat pumps can stay efficient down to lower temps. However, they all have a point where they become less efficient than resistive electric heat.
A heat pump with a sufficiently powerful resistive preheater will be at least as energy-efficient in operation as the resistive heater alone, but it's also much more complex, with a correspondingly higher up-front cost and ongoing maintenance requirements. A resistive heater can consist of little more than a solid-state heating element, a blower fan, and a mechanical thermostat; radiative heaters can even dispense with the fan, which is the least reliable part of the system. A heat pump, by contrast, additionally involves pumps, heat exchangers, and volatile fluids under pressure, generally under the management of some moderately complex logic.
Heat pumps have greater than 100 percent efficiency when compared to a regular resistive electric heater (which is already 100 percent efficient, when measured as heat out / energy in).
Everyone always forgets about the part where you're cooling down the outside...
The point is that I can heat my home by 10 degrees with a heat pump using less energy than electric resistive heating, except in specific conditions where it is too cold outside for the heat pump to function well. When I run my auxiliary heat (electric resistive heating), my bill skyrockets.
Heat pumps are no trick any more than solar panels or solar water heaters are. Resistive heat is 100% efficient while heat pumps are over unity usually 300-400% efficient although usually denoted as coefficient of performance (COP) as number ex 3 or 4. For every 1 watt put in 3-4 watts of heat come out. Real efficiency in terms of energy paid for vs energy provided to heat is what matters.
The reason they are over unity is they are taking heat from one place and moving it somewhere else. If they are pulling heat from outside air they are basically solar assisted. Technically anything above absolute zero has heat energy, even very cold outside air has plenty of heat to pump into your living space. Temperature is not heat, you can raise temperature by putting the same amount of heat in a smaller space, its like using a transmission to increase torque by lowering rpm.
Due to heat pump inefficiencies, they only make sense if you can get like a 3-4x multiplier out of them. Beyond that you break even energy-wise. Basically if it’s -10F outside, your heat pump isn’t going to be cheaper than a resistive heater. On the other hand when it’s 50F outside you do better than 4X.
Also, the $/fuel is different - if one system gets three times more joules from the same fuel, it doesn't mean it's more efficient as the other system may be using four times cheaper fuel; so a 300%-efficient heat pump is more efficient than a resistive heater but may be less efficient than a furnace burning cheap fuel.
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