Newtons Law of Cooling Suppose that an object has temperature T and is brought into a
Chapter 8, Problem 1(choose chapter or problem)
Newtons Law of Cooling Suppose that an object has temperature T and is brought into a room that is kept at a constant temperature Ta . Newtons law of cooling states that the rate of temperature change of the object is proportional to the difference between the temperature of the object and the surrounding medium. (a) Denote the temperature at time t by T (t), and explain why dT dt = k(T Ta) is the differential equation that expresses Newtons law of cooling. (b) Suppose that it takes the object 20 min to cool from 30C to 28C in a room whose temperature is 21C. How long will it take the object to cool to 25C if it is at 30C when it is brought into the room? [: Solve the differential equation in (a) with the initial condition T (0) = 30C and with Ta = 21C. Use T (20) = 28C to determine the constant k.]
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