The COP of a device, operating in a cycle is given by,
[COP] = Desired effect / Work input
In refrigerator,
the desired effect is to maintain temperature of the body A lower than the surrounding temperature.
Therefore, A refrigerator is a device, which operates in a cycle and maintains the temperature a particular body lower than the surrounding temperature.
[COP]
ref = Desired effect / Work input
[COP]
ref = Q2 / W
[COP]
H.PAnd in heat pump,
the desired effect is to maintain temperature of the body B more than the surrounding temperature.
Therefore,
[COP]
H.P. = Desired effect / Work input
[COP]
H.P = Q1 / W
and the work input is given by,
W = Q1 – Q2
From the equations of [COP]
ref and [COP]
H.P ,
[COP]
H.P. = 1 + [COP]
ref
