How to Determine the Minimum Heat Extraction from a Furnace?

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Homework Statement


Consider the heating of a house by a furnace, which serves as a heat-source reservoir at a
high temperature TF. The house acts as a heat sink at temperature T, and heat |Q| must be
added to the house to maintain this temperature. Heat |Q| can of course be transferred
directly from the furnace to the house, as is common practice. However, a third heat
reservoir is readily available, namely, the surroundings at temperature T ., which can
serve as another heat source, thus reducing the heat required from the furnace. Given that
TF = 810 K, T = 295 K, Tσ = 265 K. and |Q| = 1,000 kJ, determine the minimum amount
of heat |QF| which must be extracted from the heat-source reservoir (furnace) at TF . No
other sources of energy are available.


Homework Equations





The Attempt at a Solution


I am not sure if the way I am interpreting the question is right. There are some seemingly obvious mistakes, such as saying that the outside temperature helps reduce the amount of heat needed by the furnace.
 
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Discussion

When a refrigerator works, heat is transferred from its colder internals to its warmer surroundings, so such transfer is not impossible.
 
I agree the problem statement isn't at all clear.

It talks about the heat needed to "maintain" the temperature of the house. Normally that would suggest we are talking about power flows (eg to maintain a temperature the power flowing into and out of the house must sum to zero). However it states that the "heat" required is "1,000 kJ" which is energy not power.

It sounds like they are trying to get you to apply Carnot.