Final answer:
The lowest outdoor temperature at which a 6 kW heat pump can maintain a house's temperature depends on the heat pump's COP and the house's thermal performance. A house requiring 6,000 W to maintain an indoor temperature with an outdoor temperature of -20°C would theoretically need a heat pump with a COP of 7.3 (820 W consumption), but practical limitations typically result in lower COP values and the actual temperature will thus be higher than -20°C.
Step-by-step explanation:
To determine the lowest outdoor temperature at which a heat pump consuming 6 kW of power can maintain a specified temperature in a house, we must understand that the heat loss of the house is proportional to the temperature difference between the indoors and outdoors. From Example 6.5.3, if a house's thermal performance is 150 W/°C and we want to maintain 20°C inside while the outside is -20°C, we need to supply 6,000 W of energy. The COP (coefficient of performance) of a heat pump is affected by this temperature difference and ideally, one would expect a heat pump to use less than 2,000 W to accomplish this, suggesting a COP of about 3 as a realistic expectation due to engineering limits.
However, according to Equation 6.11, a perfect heat pump operating under the Second Law of thermodynamics could theoretically move 6,000 W of thermal energy using only 820 W, since Ɛheat ≤ 293/40 = 7.3. This would require an even higher COP, which is not feasible in practical situations. Therefore, the lowest outdoor temperature for which this heat pump can maintain the specified temperature would depend on the actual COP, but a precise calculation would require additional information about the heat pump's performance in various temperatures and the heat loss characteristics of the house.