Understanding the coefficient of performance of heat pumps

Heat pumps are sometimes portrayed as devices with an efficiency greater than 1, or “over-unit”.
This is obviously false because a yield, in physics, cannot be greater than unity. No system produces more than it consumes, and this is especially true when it comes to energy.

cop heat pump

So where did this idea about heat pumps come from?

What we are talking about with heat pumps is not energy efficiency, but a coefficient of performance (COP). This number may very well be greater than unity, and it is not synonymous with yield, as we will see.

The case of ordinary yield
When we want to heat ourselves, a form of energy is transformed into heat.

In the case of electric heating, it is electrical energy that is converted. If we consume 1000 Wh of electricity, then we will produce 1000 Wh of heat. The maximum yield will be unitary, and we recover in the form of heat that we injected in electricity.

For gas or wood heating, the calculation is the same, except that the initial energy is in the chemical form: the gas and the wood are burned, which are transformed into CO 2 and other products by releasing heat, but the amount of heat recovered will never be greater than the amount of chemical energy initially present in the product.

It’s as simple as that.

In the case of a heat pump
For a heat pump as an example, 1,000 Wh of heat can be recovered when only 100 Wh of electricity is spent. The installation’s COP is then 10.

What the COP indicates is simply that the heat pump is 10 times more economically viable for heating your home than an electric heater would be.

It can be summed up easily:

electric heating: 100 Wh consumed, 100 Wh of heat produced
heat pump with a COP of 10: 100 Wh consumed, 1,000 Wh heat produced.
For a heat pump to be profitable in use, it suffices that its COP be greater than 1, and of course, the greater the COP, the more profitable it is compared to an ordinary electric heating installation.

The question that now comes is how can we recover 1000 Wh of heat with only 100 Wh of electricity?

The answer lies in the role of a heat pump: unlike electric heating, a heat pump does not convert electricity into heat.

Instead, the heat pump moves thermal energy, which it takes outside and deposits inside the house.
And that’s what makes it so profitable: moving thermal energy doesn’t consume a lot of electrical energy. In this case with our example, moving 1000 Wh of heat only consumes 100 Wh of electricity.

As for the origin of this thermal energy outside: whether it is hot or cold, there are thermal calories in the ground and in the air.
The heat pump is a device designed to capture and transport them. The ground outside is cooled and your home is warmed. As the ground is virtually an unlimited resource of free heat, it can very well be used for heating while polluting less and reducing electricity bills.

And for information, your refrigerator works like a heat pump: from a thermodynamic point of view, the two are the same device. In the fridge, there is a circuit of fluids which captures the heat inside the fridge to evacuate it on the grid at the back of the fridge: the interior then impoverished in heat, cools and the outside is heated.

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