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SHUVRA
1 kW/ton = 3.516/COP . How to derive it? View All
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.


5 years ago - 2 months left to answer. - 1 response - Report Abuse
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Nathaniel
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


5 years ago

Source: [1] http://en.wikipedia.org/wiki/Coefficient_of_performance


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