If T is absolute temperature, the intensity of radiation from an ideal radiator is proportional to what power of T?

The intensity of radiation from an ideal radiator is described by Stefan-Boltzmann Law, which states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature. This relationship can be mathematically expressed as:

I = σT^4

where I is the intensity of radiation, σ is the Stefan-Boltzmann constant, and T is the absolute temperature in Kelvin.

This means that if the temperature of an ideal radiator is increased, the intensity of the radiation emitted increases dramatically, as it is a function of the fourth power of the absolute temperature. As a result, even small increases in temperature can lead to significant increases in radiation intensity, highlighting the quadratic nature of this relationship. This principle is crucial in various applications, including thermal radiation calculations in engineering and physics.