please explain the newtons law of cooling in detail.

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 is the temperature of the object at time t, then we have

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 , is given by

Hence,

,

which implies

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