Temperature Question

Question

A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit.



(a) If the temperature of the turkey is 149 Fahrenheit after half an hour, what is its temperature after 45 minutes?

(b) When will the turkey cool to 100 Fahrenheit? (in hours)

Answer 1

Let T(t) = temperature of the turkey t minutes after removal from the oven.

By Newton's Law of Cooling, T(t) = Ce^-kt + 75

Since T(0) = 185, Ce^-k(0) + 75 = 185. So, C + 75 = 185. Therefore, C = 110.

T(t) = 110e^-kt + 75

Since T(30) = 149, 110e^-30k + 75 = 149.

110e^-30k = 74

e^-30k = 74/110

-30k = ln(74/110)

k = 0.0132138

So, T(t) = 110e^-0.0132138t + 75

Temperature in 45 minutes = T(45)

Temperature cools to 100 when T(t) = 100