A refrigerator does not "create cold." It moves heat from a cold place (the inside of the fridge) to a hot place (the kitchen). That is the first thing to hold in your mind. The cold side gets colder because heat is being pulled out of it; the hot side gets hotter because that same heat is dumped there, plus the energy used to do the work.
If you put a hot bowl of soup inside the fridge, the fridge has to work harder. Why? Because more heat needs to be moved out. The "performance" of a fridge is simply: how much heat did I manage to pull out of the cold space, for every unit of work (electricity) I put in?
That is the intuition. You want a big "heat removed" for a small "work paid."
The precise statement
Let:
- Qc = heat extracted from the cold reservoir (the inside of the fridge). This is the "useful" effect.
- Qh = heat dumped into the hot reservoir (the kitchen). This is always larger than Qc.
- W = work input (electrical energy consumed by the compressor).
From the first law of thermodynamics (energy conservation), for a complete cycle:
Qh=Qc+W
The work you put in ends up as extra heat added to the hot side. So the Coefficient of Performance (COP) of a refrigerator is defined as:
COPR=What you payWhat you want=WQc
Using W=Qh−Qc, we get the standard form:
COPR=Qh−QcQc
COP is not efficiency. Efficiency (for a heat engine) is always less than 1. COP for a refrigerator is always greater than 1 (often 2–6 for real fridges). Why? Because Qc can be several times larger than W. You are moving heat, not converting it into work.
A concrete example
Suppose a fridge extracts 200 J of heat from the inside (Qc=200 J) and dumps 250 J into the kitchen (Qh=250 J). Then the work done is W=250−200=50 J.
COP=50200=4
This means: for every 1 J of electrical energy you pay for, the fridge moves 4 J of heat out of your food. That is a COP of 4 — quite good.
If the fridge were perfect (impossible), it would move heat with zero work, and COP would be infinite. Real fridges have COP values between 2 and 6, depending on the temperature difference they have to work against.
A common mistake: thinking COP = Qh/W or Qh/(Qh−Qc). That is the COP of a heat pump (used for heating), not a refrigerator. For a fridge, the numerator is always Qc, the heat removed from the cold space.
Why the formula makes physical sense …