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teja reddy Grade: 10
        

please explain the newtons law of cooling in detail.

7 years ago

Answers : (1)

Vijay Luxmi Askiitiansexpert
357 Points
										

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.

7 years ago
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