Answer to Question #172560 in Physics for Diocos

Question

At what net rate does heat radiate from a 244-m² black roof on a night when the roof’s temperature is 20.34ºC and the surrounding temperature is 37.13 ºC? The emissivity of the roof is 0.379

Answer 1

Convert temperature in degree Celsius to Kelvin:

T₂=20.34+273.15=293.49 K,

T₁=37.13+273.15=310.28 K.

The net rate of heat radiation is

$$\frac{Q}{t}=A\epsilon\sigma(T_2^4-T_1^4),\\\space\\ \frac{Q}{t}=244·0.379·5.67·10^{-8}(293.49^4-310.28^4)=\\=-9700\text{ W}.$$