In the winter, your roof is warmer than the surrounding air -- especially at nig
ID: 1482500 • Letter: I
Question
In the winter, your roof is warmer than the surrounding air -- especially at night. That's why you often see a rising cloud of steam above houses on cold and damp winter nights ... Suppose that the temperature of your 275-m2 roof is 22°C, while that of the nighttime air is only 5°C. The roof is black so its emissivity is 0.897. (a) At what rate does your roof radiate heat to its surroundings? script Prad = kW (b) At what rate does it absorb heat from its surroundings? script Pabs = kW (c) The roof is Correct: Your answer is correct. radiant energy at a net rate of kW.
Explanation / Answer
let,
area of the roof, A=275 m^2
temeperature T1=22 oC =295 K
temeperature T2=-5 oC =268 K
e is emissivity e=0.897
stefan constant, sigma=5.67*10^-8 W*m^2/K4
power P=Q/t=e*sigma*A*T^4
a)
P_radiate=e*sigma*A*T1^4
=(0.897)*(5.67*10^-8)*(275)*(295)^4
=105.92*10^3 W
=105.92 kW <---------------------------------
b)
P_absorb=e*sigma*A*T2^4
=(0.897)*(5.67*10^-8)*(275)*(268)^4
=72.15*10^3 W
=72.15 kW <---------------------------------