Question

Consider a surface at 0°C that may be assumed to be a black body in an environment at 25°C. If 300 W/m² of radiation is incident on the surface the radiosity of this black surface is:
1. 0 W/m2
2. 132 W/m2
3. 300 W/m2
4. 315 W/m²

Answer 1

Correct Answer - Option 4 : 315 W/m²

Concept:

Radiosity(J):

It is a total rate of energy leaving from the surface to all direction for all longer wavelength per unit surface area.

For black body, α = 1 and ρ = τ = 0.

Mathematically, Radiosity is represented by

J = ρG + E + τG

where, G = Irradiation, E = Emissive power

Calculation:

Given:

G = 300 W/m², T_s = 0°C = 273 K, T_o = 25°C = 25 + 273 = 298 K, J = ?

Now, we know that

J = ρG + E + τG

J = E, (ρ = τ = 0)

According to Kirchhoff’s law, α = ϵ

∴ J = E = ϵ σ T_s⁴ = 1 × 5.67 × 10^-8 × 273⁴ (∵ α = ϵ =1) (W/m²)

∴ J = 314.944 W/m²