Dual Nature Of Radiation And Matter

The problem involves two spherical black bodies radiating the same amount of heat per second. According to Stefan-Boltzmann Law, the power radiated by a spherical black body is given by:

where is the Stefan-Boltzmann constant, is the surface area, and is the temperature of the black body.

For a sphere, the surface area . Thus, the power radiated by each sphere can be given as:

Since both bodies radiate the same amount of heat per second, we equate and :

We can cancel and from both sides:

Rearranging the equation, we get:

Taking the fourth root on both sides:

Now, if we assume the relation , it implies:

Thus, .

Since both sides match, the correct relation is indeed .