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

1 Answer

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.