Question

A black body at 1100 oc surrounding at 200oc find heat loss per unit area by radiation.

Answer 1

The heat loss per unit area by radiation is 1.043 × 10⁵ W/m².

A black body at 1100°C surrounding at 200°C.

We have to find the heat loss per unit area by radiation.

Stefan-Boltzmann's law “ It says that total radiant heat energy emitted from a surface is proportional to fourth power of its absolute temperature.”

i.e., E = σT⁴ ,

• E is radiant heat energy per unit area per unit time.
• σ is Stefan-Boltzmann's constant. σ = 5.67 × 10^-8 W/m²/K⁴
• T is the absolute temperature.

condition : If temperatures of source and surrounding are given,

then heat loss from source to surrounding is given by, E = σ(T⁴ - T₀⁴)

where T₀ is absolute temperature of surrounding.

here, T = 1100°C = 1100 + 273 = 1373K

T₀ = 200°C = 200 + 273 = 473K

now, E = 5.67 × 10^-8(1173⁴ - 473⁴) W/m²

= 5.67 × 10^-8(1.89 × 10¹² - 5 × 10¹⁰) W/m²

= 5.67 × 10^-8 × 1.84 × 10¹² W/m²

= 5.67 × 1.84 × 10⁴ W/m²

= 10.43 × 10⁴ W/m²

= 1.043 × 10⁵ W/m²

Therefore the heat loss per unit area by radiation is 1.043 × 10⁵ W/m².