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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

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Answer:

D.) 1.4 kW

Explanation:

[tex]\sigma[/tex] = Stefan-Boltzmann constant = [tex]5.67\times 10^{-8}\ W/m^2K^4[/tex]

[tex]\epsilon[/tex] = 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

[tex]P=\sigma\epsilon AT^4\\\Rightarrow P=5.67\times 10^{-8}\times 1\times 1.25\times 373.15^4\\\Rightarrow P=1374.12694\ W=1.37412694\ kW\approx 1.4\ kW[/tex]

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

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