Question

The spectral distribution of the radiation emitted by a diffuse surface may be approximated as follows. HW 2 Q2 (a) What is the total emissive power? (b) What is the total intensity of the radiation emitted in the normal direction and at an angle of 30° from the normal? (c) Determine the fraction of the emissive power leaving the surface in the directions π/4 ≤ θ ≤ π/2.

Answer 1

Answer:

a) 2000 W/m²  ; b) 636.94 W/m².sr ; c) 0.5

Explanation:

a)

The formula for calculation of total emissive power is:

Total emissive power = E = $\int\limits^\alpha_0$ E'λdλ

                                   = $\int\limits^a_0$(0)dλ + $\int\limits^b_a$(100)dλ + $\int\limits^c_b$(200)dλ + $\int\limits^d_c$(100)dλ $\int\limits^e_d$(0)dλ

where a = 5; b = 10; c = 15; d = 20; e = 25

                                   = 0 +100(10-5) + 200(15-10) +100(20-15) + 0

                                   = 2000 W/m²

b)

The formula for total intensity of radiation is:

I$_{e}$ = E/π = 200/3.14 = 636.94 W/m².sr  

c)

Fo submissive power leaving the surface in range π/4 ≤θ≤π/2

[E(π/4 ≤θ≤π/2)]/E = $\int\limits^f_0$$\int\limits^g_0$$\int\limits^i_h$ Icosθsinθ dθdΦdλ

where f = infinity, g=2π, h=π/4, i=π/2

By simplifying, we get

                           = (-1/2)[cos(2π/2)-cos(2π/2)]

                           = -0.5(-1-0)

                           =0.5