Question

Consider a blackbody that radiates with an intensity I1I1I_1 at a room temperature of 300K300K. At what intensity I2I2I_2 will this blackbody radiate when it is at a temperature of 400K400K ? Express your answer in terms of I1I1I_1.

Answer 1

`I_2 = 3.16 I_1`

Step-by-step explanation:

given,

Intensity radiated by black body= I₁

room temperature = 300 K

Intensity radiated, I₂ = ?

At temperature = T₂ = 400 K

now,

Intensity of radiation, I = σ T⁴

now,

`(I_1)/(I_2)=(T_1^4)/(T_2^4)`

`(I_2)/(I_1)=(T_2^4)/(T_1^4)`

`I_2=I_1(T_2^4)/(T_1^4)`

`I_2=I_1(400^4)/(300^4)`

`I_2 = 3.16 I_1`

hence, Radiation Intensity at 400 K is equal to I₂ = 3.16 I₁