1 kW/ton = 3.516/COP . How to derive it?
In Refrigeration Course, I have found this equation. But I can’t derive this. You see, how did I approach :
COP=(Refrigeration Effect) / (Work Input)
COP is dimensionless. So, I can write:
COP=(1 kW of Refrigeration Effect) / (1 kW of Work Input)
So, (1 kW of Work Input) / (1 kW of Refrigeration Effect) =1/COP
or, (3.516 kW of Work Input) / (3.516 kW of Refrigeration Effect) =1/COP
or, (3.516 * 1 kW of Work Input) / ( 1 Ton of Refrigeration Effect) = 1/COP
[3.516 kW = 1 Ton of Refrigeration Effect]
or, (3.516 * 1 kW) / ( 1 Ton) = 1/COP
which implies: 1 kW/ton = 1/(COP * 3.516)
What is the error in my calculation? If anybody knows, please help me. It is driving me crazy. Thanks.
Actually based on your equations
COP = 3.516 kW/ton of Cooling / 1.0 kW/ton of work
This is based on the definition of the cooling CoP
COP =|deltaQ| / |deltaW|
deltaQ = heat change in the reservoir of interest
deltaW = energy consumed by the heat pump.
For more information about how to derive CoP go to [1] Wikipedia.
Niel
