Tässä muualla laskettu esimerkki ei-triviaaleilla luvuilla. Ne eivät kuitenkaan muuta lopputulosta:
"Let's use some concrete, but made up, numbers:
Heat pump A has environmental heat input of >=4kW, electrical input of 1kW, and heat output is 5kW. COP=5.
Heat pump B has environmental heat input of 5kW (from HP A), electrical input of 1kW, and heat output is 5kW. COP=5
Notice the final COP is not 5; it's 2.5.
Now, you're right, with that information it looks like you can just replace HP B with a resistive heater (or nothing). So let's throw in flow and temperature rise, and pretend they're coupled with water (it doesn't actually matter whether it's a separate fluid, none at all, or the refrigerant itself... it works out the same).
HP-A outputs 40°C water and HP-B output 80°C. Let's assume both outputs drop 5°C across the heat exchanger, so the output of HP-A is raising water 5°C with 5kW, water has 4.2 Ws/g°C (J=Ws), we want g/s so 5000 W / 5 °C / 4.2 = 238 g/s of water flow.
Let's state that again: HP-A outputs 40°C water at a rate of 238 g/s when the return temperature is 35°C.
But now let's apply 1kW of heating to 40°C water at a rate of 238 g/s: 238 g/s × 4.2 × 1000 W = 1 °C. That's no where near 80°C!
Okay, how much water could we raise from 40°C to 80°C? 1000W / 4.2 / 40°C = 6.0 g/s. Except, HP-A has a return temperature of 35°C, so to get the same average temperature of 77.5°C, we need an initial output temperature of 120°C (assume it was still water at this point), so our output rate is even less: 1000W / 4.2 / 85°C = 2.8 g/s flow.
But now calculate how much HP-A is putting out: it's only heating 2.8 g/s of water, not 238 g/s. It's only outputting 1.2% of 5kw or 59W. And our actual power output is 1059W at an average temperature of 77.5°C and with a COP=1.046, much worse than our 2.5 using two heat pumps.
It's actually possible to get the same output, if HP-A's output temperature was 79°C and you added a 1kW heater it'd be equivalent to using HP-B and an overall COP=2.5. But you wouldn't do that."
