Suppose that as a body cools, the temperature of the
Chapter 3, Problem 3.1.110(choose chapter or problem)
Suppose that as a body cools, the temperature of the surrounding medium increases because it completely absorbs the heat being lost by the body. Let T(t) and Tm(t) be the temperatures of the body and the medium at time t, respectively. If the initial temperature of the body is T1 and the initial temperature of the medium is T2, then it can be shown in this case that Newtons law of cooling is dTdt k(T Tm), k 0, where Tm T2 B(T1 T), B 0 is a constant. (a) The foregoing DE is autonomous. Use the phase portrait concept of Section 2.1 to determine the limiting value of the temperature T(t) as t : . What is the limiting value of Tm(t) as t : ? (b) Verify your answers in part (a) by actually solving the differential equation. (c) Discuss a physical interpretation of your answers in part (a). 8.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer