The temperature of a cup of coffee obeys Newtons law of cool

The temperature of a cup of coffee obeys Newton\'s law of cooling. The initial temperature of the coffee is 150 degree F and one minute later, it is 135 degree F. The ambient temperature of the room is 70 degree F. If T(t) represents the temperature of the coffee at time t, the correct differential equation for the temperature with side conditions is Select the correct answer. a. dT/dt = K(T - 135) b. dT/dt = K (T - 150) C. dT/dt = K(T - 70) D. dT/dt = T (T - 150) e. dT/dt = T (T - 70) In the previous problem, after a long period of time, the temperature of the coffee approaches Select the correct answer. a. 120 degree F b. 100 degree F c. 70 degree F d. 65 degree F e. 0 degree F

Solution

6

c)

In Newton\'s law of cooling rate of cooling is directly proportional to the difference in temperature of object and temperature of surrounding

7

c)

The object cools down and approaches the temperature of the surrounding which is 70 F in given problem. In practical life this happens in finite time but in this approximate mathematical model this happens in infinite time.