Coefficients of Performance (AQA A Level Physics)

Coefficients of Performance

• As mentioned in Heat Pumps & Refrigerators, the efficiency of a reversed heat engine depends on its purpose

• Therefore a coefficient of performance (COP) is used to measure their effectiveness instead

  • It is not a measure of efficiency, as it can be greater than 1 

• The COP is a measure of how effective a reversed heat engine is at transferring heat per unit of work done

  • E.g. A COP of 7 is 7 J of heat energy is transferred per 1 J of work done

• The COP of a refrigerator is defined by:

• Where:

  • Q_C = energy extracted from the cold space (J)

  • Q_H = energy delivered to the hot space (J)

  • W = work inputted (J)

  • T_H = temperature of hot space (K)

  • T_C = temperature of the cold space (K)

• The COP of a heat pump is defined by:

• Since , the COPs could be written in terms of each other:

• Because the COP is a ratio it has no units

• Since Q_H > Q_C, this means

• Heat pumps are used instead of conventional electric or gas heaters for large-scale buildings because the energy transferred by a heat pump exceeds the work done on the pump

  • An electric or gas heater will at most convert 1 J of energy per 1 J of work done, so would be far more expensive to run on large scales