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

Answer:

$I_2 = 3.16 I_1$

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,

$\dfrac{I_1}{I_2}=\dfrac{T_1^4}{T_2^4}$

$\dfrac{I_2}{I_1}=\dfrac{T_2^4}{T_1^4}$

$I_2=I_1\dfrac{T_2^4}{T_1^4}$

$I_2=I_1\dfrac{400^4}{300^4}$

$I_2 = 3.16 I_1$

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