Question

Consider a black sphere of radius R at temperature T which radiates to distant black surroundings at T = 0 K. The sphere is surrounded by nearby heat shield in the form of black shell whose temperature is determined by radiative equilibrium -

• A. The temperature of the shell is $\frac{T}{\sqrt{2}}$
• B. The temperature shell is $\frac{T}{(2)^{1/4}}$
• C. Total power radiated to the surroundings remains the same
• D. Total power radiated to the surroundings is reduces to one fourth of the initial value

Answer 1

Answer: (B)

The temperature shell is $\frac{T}{(2)^{1/4}}$

Answer 2

Rate of energy absorbed by shell = Rate of energy radiated by shell

H – H₁ = H₁

H₁ = $\frac{H}{2}$ ; power radiated to the surroundings

T₁⁴ = $\frac{T^{4}}{2}$

T₁ = $\frac{T}{(2)^{1/4}}$