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Preliminary remarks

An aluminum beam brought from the outside cold into a machine shop where the regular normal temperature is maintained warms up to the temperature of the surrounding air. A hot silver ingot immersed in water cools to the temperature of the surrounding water.

In situations like these, the rate at which an object's temperature is changing at any given time is approximately proportional to the difference between its temperature and the temperature of the surrounding medium. This observation is sometimes called the Newton's Law of Cooling, although, as in the case with the aluminum beam, it applies to warming as well.

An equation representing this law can be written as
\begin{maplelatex}
\begin{displaymath}
T - T_s = (T_0 - T_s)e^{-kt},\hspace*{2.8in}{(5)}\end{displaymath}\end{maplelatex}
where T is the temperature of the object at time $t, \;T_s$ is the surrounding temperature, T0 is the value of T at time zero.



Christine M Palmer
9/23/1998