A roast turkey is taken from an oven when its temperature has reached 195 Fahrenheit and is placed on a table in a room where the temperature is 65 Fahrenheit.

Question

(a) If the temperature of the turkey is 150 Fahrenheit after half an hour, what is its temperature after 45 minutes? _______ Fahrenheit.

(b) When will the turkey have cooled to 110 Fahrenheit? ___ hours.

Answer 1

Assuming Newtons law of cooling: (T - T_Amb)/(T_i - T_amb) = e^-kt This allows the left hand side to decay from 1 to 0. The equation follows from the rate of heat flow being proportional to the difference in temperature between the turkey and the room. (amb = ambient, i = initial)

a) You can solve for k given all the other data. Then you solve for T, knowing k

b) You solve for t given all the other data.

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