Consider the heating of a house by a furnace, which serves as a heat source reservoir at a high temperature T_F. The house acts as a heat sink reservoir at temperature T, and heat |Q| must be added to the house during a particular time interval to maintain this temperature. Heat |Q| can of course be transferred directly from the furnace to the house, as is the usual practice. However, a third heat reservoir is readily available, namely, the surroundings at temperature T_σ, which can serve as another heat source, thus reducing the amount of heat required from the furnace. Given that T_F = 810 K, T = 295 K, T_σ = 265 K, and |Q| = 1000 kJ, determine the minimum amount of heat |Q_F| which must be extracted from the heat-source reservoir (furnace) at T_F. No other sources of energy are available.