Question

Consider a blackbody that radiates with an intensity I1 at a room temperature of 300 K. At what intensity I2 will this blackbody radiate when it is at a temperature of 400 K?

Answer 1

I₂ = 3.16 I₁

Step-by-step explanation:

A blackbody is a substance that absorbs radiation of all wavelengths and radiates in a continuous spectrum at all wavelengths. It is given the name blackbody because an object that absorbs light at all wavelengths appears black to the human eye.

The total intensity I (the average rate of radiation of energy per unit surface area) emitted from a blackbody was shown to be proportional to the fourth power of its temperature:

I = бT⁴.

This is called the Stefan-Boltzmann law for a blackbody. The constant of proportionality sigma is known as the Stefan-Boltzmann constant.

So, I is directly proportional to T⁴

∴ I₂/I₁ = T⁴₂/T⁴₁

=400⁴/300⁴ = 3.16

So, I₂ = 3.16 I₁