Consider the heating of a house by a furnace, which serves as a heat-source rese
ID: 2991568 • Letter: C
Question
Consider the heating of a house by a furnace, which serves as a heat-source reservoir at ahigh temperature TF. The house acts as a heat-sink reservoir at temperature T , and heat
I Q I must be added to the house during a particular time interval to maintain this temperature.
Heat I Q I 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,, which can serve as another heat source, thus reducing the amount
of heat required from the furnace. Given that TF = 810 K, T = 295 K, T, = 265 K, and
I Q I = 1000 kJ, determine the minimum amount of heat I QFI which must be extracted
from the heat-source reservoir (furnace) at TF . No other sources of energy are available.
Explanation / Answer
Heat flows from higher temperature to lower temperature and the rate of flow is proportional to the difference in temperatures.
heat transfer from furnace to the room
Q= K(Tf-T) where K is a constant
For the third reservoir to tranfer heat to the room it must be maintained at a temperature not less than
heat need to be transfred to the third reservoir = K(T-Ts) = Q(T-Ts)/(Tf-T) = 1000*(295-265)/(810-295) = 58.25
By maintaining the third reservoir at T(295) the required temperature, the room will be maintained at the required temperature, ensure required flow of heat to the room.
Heat need to be extracted from the furnace = 58.25 J
Note: the assumption here is material of the surroundings and the room have same heat properties .