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Answer to Question #12237 in Other Math for joe

Question #12237
A roasted turkey is taken from the oven when its temperature has reached 185 degrees F and is places on a table in a room where the temperature is 75. A) if the temperature of the turkey is 150 after half an hour what is the temperture after 45 min? B) When will the turkey cool to 100 degrees?
Expert's answer
A) if the temperature of the turkey is 150 after half an hour what is the temperture after 45 min?

Let's assume that the turkey temperature decreases by the next law:

T(t) = c(T(t)-Tr)t,& (1)

or equally

T(t) = - c*Tr*t / (1-c*t), (2)

where T is the current turkey temperature, T0 is initial turkey temperature, Tr is the room temperature, c is the cooling coefficient and t is the time since turkey was taken out from the oven. Let's find c. We know that T0 = 185°F and after half an hour it decreased to 150°F. So,

(1) ==> 150 = c(150-75)0.5 ==> c = 4 units/hour.

So, after 45 minutes the temperature of a turkey will be

(2) ==> T(3/4 hour) = - 4*75*3/4 / (1-4*3/4) =& 112.5°F.

B) When will the turkey cool to 100 degrees?

(1) ==> 100 = 4(100-75)t ==> t = 1 hour.

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