The coefficient of performance or COP (sometimes CP) of a heat pump is the ratio of the heating or cooling provided over the electrical energy consumed. The COP was created to compare heat pump systems according to their energy efficiency.
A level of performance that describes a process that uses the lowest amount of inputs to create the greatest amount of outputs. Efficiency relates to the use of all inputs in producing any given output, including personal time and energy.
COP of Heat Pump = 1 + COP of the Refrigerator
The COP of the refrigerator and air-conditioner can be less than one or greater than one. The above formula also shows that the COP of the heat pump can never be less than one; it is always more than one.
Its says how effectively the refrigerator or air conditioner is working. The function of the refrigerator and AC is to move the heat from the low temperature reservoir to the high temperature reservoir (against the law of thermodynamics that says that heat flows from high temp. to low temp.). The COP says how effectively the refrigerator or AC performs this function. It says the amount of power required by the machine to move certain quantity of heat from low temp. to high temp.
The efficiency is related with automobile engines, boilers etc that produce power from the fuel. They convert energy from one form to the other, while refrigerator moves the energy from low temp. to high temp. So the efficiency says how effectively the machine is converting the energy from fuel to the power.
The COP can be more that one since the heat transferred can be more than power required by the refrigerator but the efficiency can never be more than one since the power generated by engine cannot be more than the total heat content of the fuel.