Suppose you have just a cup of freshly brewed coffee with temperature 90 degree

Question

Suppose you have just a cup of freshly brewed coffee with temperature 90 degree C in a room where the computer is 20 degree C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation dT/dt = k(T - T room) where T room = 20 is the room temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 2 degree C per minute when its temperature is 60 degree C. What is the limiting value of the temperature of the coffee? T(t) = What is the limiting value of the rate of cooling? dT/dt = Find the constant k in the differential equation. k =

Explanation / Answer

a) as t -> , the Temperature of the coffee approaches the temperature of the room.

b) since the temp of the coffee goes to the temp of the room, dT/dt = k(T-Troom) = 0

c) dT/dt = -2 = k(60 - 20) = k(40)

k = -2/40 = -1/20 = -0.05

remember the coffee is cooling so the change in temperature is negative.

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