Question

A sphere of surface area 1.25 m2 and emissivity 1.0 is at a temperature of 100°C. At what rate does it radiate heat into empty space? (σ = 5.67 × 10-8 W/m2 ∙ K

A.) 9.9 mWB.) 3.7 WC.) 7.1 WD.) 1.4 kW

Answer 1

D.) 1.4 kW

Step-by-step explanation:

`\sigma` = Stefan-Boltzmann constant =
`5.67* 10^(-8)\ W/m^2K^4`

`\epsilon` = Emissivity = 1

T = Temperature = 100+273.15 = 373.15 K

A = Surface area = 1.25 m²

According to Stefan-Boltzmann Law radiated power is given by

`P=\sigma\epsilon AT^4\\\Rightarrow P=5.67* 10^(-8)* 1* 1.25* 373.15^4\\\Rightarrow P=1374.12694\ W=1.37412694\ kW\approx 1.4\ kW`

The at which it radiates heat into empty space is 1.4 kW