Chapter 19 - Exercises and Problems - Page 362: 34

The coefficient of performance (COP) of a heat pump is defined as the ratio of the heat output to the energy input. A higher COP indicates a more efficient heat pump. To determine the minimum acceptable COP for the heat pump, we need to find the energy input required to produce the ENV average of 6.85 kW. Assuming that the heat pump is the only source of heat and that it operates at 100% efficiency (i.e., no energy losses), the energy input required to produce 6.85 kW of heat is: E_in = 6.85 kW / COP We know that the photovoltaic system will supply 2.32 kW of electric power on average. Therefore, the energy input required from the heat pump to produce the remaining 4.53 kW (6.85 kW - 2.32 kW) of heat must be less than or equal to the energy output of the photovoltaic system: E_in ≤ 2.32 kW Substituting the first equation into the second equation, we get: 6.85 kW / COP ≤ 2.32 kW Solving for the minimum acceptable COP, we get: COP ≥ 6.85 kW / 2.32 kW = 2.96 Therefore, the minimum acceptable COP for the heat pump is 2.96 if the photovoltaic system supplies its energy.

The coefficient of performance (COP) of a heat pump is defined as the ratio of the heat output to the energy input. A higher COP indicates a more efficient heat pump. To determine the minimum acceptable COP for the heat pump, we need to find the energy input required to produce the ENV average of 6.85 kW. Assuming that the heat pump is the only source of heat and that it operates at 100% efficiency (i.e., no energy losses), the energy input required to produce 6.85 kW of heat is: E_in = 6.85 kW / COP We know that the photovoltaic system will supply 2.32 kW of electric power on average. Therefore, the energy input required from the heat pump to produce the remaining 4.53 kW (6.85 kW - 2.32 kW) of heat must be less than or equal to the energy output of the photovoltaic system: E_in ≤ 2.32 kW Substituting the first equation into the second equation, we get: 6.85 kW / COP ≤ 2.32 kW Solving for the minimum acceptable COP, we get: COP ≥ 6.85 kW / 2.32 kW = 2.96 Therefore, the minimum acceptable COP for the heat pump is 2.96 if the photovoltaic system supplies its energy.