Final answer:
To find the lowest outdoor temperature at which a 4 kW heat pump can maintain a house at 24°C, calculate the maximum temperature difference the pump can handle given its power output and the house's heat loss rate; the result is -20.8°C, making option d. -14.7°C the closest choice.
Step-by-step explanation:
The student has asked about determining the lowest outdoor temperature at which a heat pump can maintain the indoor temperature of a house at 24°C, given the rate at which the house loses heat and the power input of the heat pump. To answer this, we first need to convert the power input of the heat pump from kilowatts to kilojoules per hour since the heat loss rate is given in kilojoules per hour. The heat pump provides 4 kW, which is equivalent to 4 kJ/s, and when converted to hours, that's 4 kJ/s × 3600 s/h = 14400 kJ/h.
Next, we'll calculate the temperature difference at which the heat pump can no longer compensate for the house's heat loss. The house loses 4500 kJ/h per °C difference. If the heat pump provides 14400 kJ/h at maximum, the temperature difference it can handle is 14400 kJ/h ÷ 4500 kJ/h/°C = 3.2°C. Since the indoor temperature is 24°C, the outdoor temperature at which the heat pump will just barely maintain the indoor temperature is 24°C - 3.2°C = 20.8°C. To include a minus sign as requested, the answer is -20.8°C, which means option d. -14.7°C is the closest correct choice from the given options.