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.

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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Answer 2

Benjamin Asiedu

Stefan's law and Newton's law of cooling are related in the sense that they both describe the transfer of heat between objects and their surroundings. While Stefan's law specifically deals with the rate at which a black body radiates energy as a function of its temperature, Newton's law of cooling describes how the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Both laws involve heat transfer mechanisms and can be used to analyze thermal processes.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.