Question

Suppose you are considering renting an apartment in a building in which the tenants are required to pay the cost of heating their apartments. The building has several apartments, each occupying an entire floor of the building. The building has a flat roof. You are attracted to the apartment on the top floor because of the view but your friend tells you that the heat bills will be higher for that apartment than for the ones on the lower floors.

a. [3pts] Is your friend likely to be right? Explain why or why not in terms of the expected thermal energy flows in and out of the apartments.

b. [4pts] Defend your answer to a. by calculating the amount of energy required to heat the top and lower apartments for a year in btu. Include the lowest apartment assuming that it is just above the ground (no basement below it). Suppose that the floor area of each apartment is 900 sq ft (30ft x 30ft) and that the height from one floor to the next is 10ft. Use 8500 as the number of ’degree days’ in Minnesota (Figure 5.12 and definition near the top of p. 137) and the R values given in Table 5-1 of the book (1978 values).

c. [3pts] Use the answer you got in b. to calculate the difference in cost (if any) between heating the top apartment for a year ,heating a lower apartment for year, and heating the ground floor apartment for a year, supposing that the cost of gas heating is $0.80 per ’therm’. 1 therm=100,000 btu.

Answer 1

(a) Yes, your friend is likely to be right. Other than the top floor has only four side walls will get in contact with outside weather condition/temperature. But, for the top floor, four side wall plus the roof will get in contact with outside. Hence, more amount of heat needed to keep the temperature of the room at top floor than other apartment. If the temperature of the outside environment id less than the room temperature, then outflow of heat will be more for the apartment at the top floor due to the more amount of areas in contact with outside environment.

(b) The area of the side wall for one apartment is

The area of the roof of the apartment is 900 sq. ft which is equal to the floor area.

Therefore, the area in contact with the outside environment for top floor apartment is (1200 sq. ft + 900 sq. ft) or 2100 sq. ft.

And for other apartment, it is only 1200 sq. ft.

But in this problem, the R value is not supplied, so I can not calculate the amount of energy required to heat the top and lower apartments for a year in btu. You can calculate by the idea given above.

(c) Similarly, by getting the answers in (b), you can easily calculate the difference in cost (if any) between heating the top apartment for a year ,heating a lower apartment for year, and heating the ground floor apartment for a year.

Let us consider Q btu amount of heat needed for an apartment. Hence the value of heat in the unit of "therm" is Q/100000 (as 1 therm = 100,000 btu). Hence the cost for heating is Q*0.08/100000 $ ($0.80 per ’therm’).