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please explain the newtons law of cooling in detail.

please explain the newtons law of cooling in detail.

Grade:10

1 Answers

Vijay Luxmi Askiitiansexpert
357 Points
11 years ago

Hi Teza,

From experimental observations it is known that (up to a ``satisfactory'' approximation) the surface temperature of an object changes at a rate proportional to its relative temperature. That is, the difference between its temperature and the temperature of the surrounding environment. This is what is known as Newton's law of cooling. Thus, if tex2html_wrap_inline27 is the temperature of the object at time t, then we have

displaymath31

where S is the temperature of the surrounding environment. A qualitative study of this phenomena will show that k >0. This is a first order linear differential equation. The solution, under the initial condition tex2html_wrap_inline37 , is given by

displaymath39

Hence,

displaymath41,

which implies

displaymath43

This equation makes it possible to find k if the interval of time tex2html_wrap_inline47 is known and vice-versa.

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