Question

The roof of a house has three layers: (1) 2 inch thick pine, (2) 4 inches of fiberglass insulation and (3) 0.1 inch thick Asphalt shingles. Calculate the rate of flow of heat (BTU/hour) through the roof. The temperature inside the house is 700F and the temperature outside is 300F. The R/inch for pine is 1.28, the R/inch for fiberglass is 3.0 and the R/inch for Shingles is 4.0. Take the area of the roof to be 500 square feet. The Unit of R is mixed: ft2 . 0F.h/BTU

Answer 1

the rate of flow of heat through the roof is 45616.858 BTU/hr

Step-by-step explanation:

Given the data in the question;

pin thickness
`t_p` = 2 in

fiber glass thickness
`t_f` = 4 in

Asphalt shingles thickness
`t_a` = 0.1 in

R/inch for pine = 1.28

R/inch for fiberglass = 3.0

R/inch for Shingles = 4.0

Temperature inside the house
`T_{inside` = 700 F

Temperature outside the house
`T_{outside` = 300 F

area of the roof A = 500 ft²

we calculate the total Resistance;

R = ( 2 × 1.28 ) + ( 4 × 3.0 ) + ( 0.1 × 4.0 )

R = 2.56 + 12 + 0.4

R = 14.96

Now, we determine the rate of heat flow;

dQ/dt = ΔT(A) / R

⇒ (
`T_{inside` -
`T_{outside` )A / R

we substitute

⇒ (( 700 - 300 ) × 500 ) / 14.96

⇒ ( 400 × 500 ) / 14.96

⇒ 200000 / 14.96

⇒ 13368.98 watt

we know that 1 watt = 3.412142 BTU/hr

⇒ ( 13368.98 × 3.412142 ) BTU/hr

⇒ 45616.858 BTU/hr

Therefore, the rate of flow of heat through the roof is 45616.858 BTU/hr