Newton’s law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. Thus, if T is the temperature of the object after t hours and T_M is the (constant) temperature of the surrounding medium, then

where k is a constant. Use this equation in Exercises.

According to the solution of the differential equation for Newton’s law of cooling, what happens to the temperature of an object after it has been in a surrounding medium with constant temperature for a long period of time? How well does this agree with reality?

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dT dt = || -K(T-TM),