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.

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