Question

How are Stefan's law and Newton's law of cooling related?

Answer 1

Newton's law of cooling is a consequence of Stefan's law.

Explanation:

Let `T` and `T'` be the temperature of the body and the surroundings.
Then by Stefan;s law rate of heat loss of body is given by,
`Q= sigma(T^4-T'^4)`
`=sigma(T^2-T'^2)(T^2-T'^2)`
`=sigma(T-T')(T+T')(T^2+T'^2)`
`=sigma(T-T')(T^3+T^2T'+T T'^2+T'^3)`

If the excess temperature `T-T'` be small, then `T` and `T'` are nearly equal. So,
`Q=sigma(T-T')*4T'^3`
`=beta(T-T')`

So, `Q prop (T-T')` which is Newton's law of cooling.