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

1 Answer
aniruddho r. · Aritra G.
Oct 14, 2015

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.

Related questions
See all questions in Stefan's Law
Impact of this question
4572 views around the world
You can reuse this answer
Creative Commons License