Suppose the ratio of the actual energy entering the room to the work done by the device's motor is 10.0% of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor given that the inside temperature is 24.0°C and the outside temperature is -2.00°C.
A theoretical heat pump operates using the Carnot cycle. The ratio of what we want to what we pay for in a refrigeration cycle is called coefficient of performance (COP). For a refrigeration cycle, operated as a heat pump with the indoor heat exchanger as the heat output device, the ideal COP (that which occurs in the Carnot Cycle) is as follows: COP_HPcarnot = 1 + 1/(T_H/T_L - 1) Temperatures must be in either Kelvin or Rankine scales. With the given fraction of ideal efficiency (f), the actual COP is: COP_HPactual = f*COP_HPcarnot thus: COP_HPactual = f*(1 + 1/(T_H/T_L - 1)) Data: f:=0.1; T_H:=297.15 K; T_L:=271.15 K; Result: COP_HPactual = 1.143 This corresponds to COP_HPactual = Q_dot_out/W_dot_in where Q_dot_out is the heat output of the system to the room, and W_dot_in is the work required for compressor operation.
