5.31. Consider the heating of a house by a furnace, which serves as a heat-sourc

Question

5.31. 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 reservoir at temperature T, and heat IQI must be added to the house during a particular time interval to maintain this temperature. Heat IQI 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 Tsigma. 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, Tsigma = 265 K, and IQI = 1,000 kJ, determine the minimum amount of heat I QF I 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 .

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.