In Exercises 65–68 in the previous section, we saw that Newton’s Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. This leads to the differential equation

where T is the temperature of the object after time t, T_M is the temperature of the surrounding medium, and k is a constant. In the previous section, we solved this equation by separation of variables. Show that this equation is also linear, and find the solution by the method of this section.

Exercises 66

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?

Transcribed Image Text:

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