Question

A pie is removed from a 375°F oven and cools to 215°F. after 15 minutes in a room at 72°F. How long (from the
time it is removed from the oven) will it take the pie to
cool to 120 f ?

Answer 1

By Newton's Law of Cooling:
dT/dt = k(T - 72)
-160 = 303k
k = -160/303
dt/dT = 1/k * 1/(T - 72)
t + c = 1/k * ln |T - 72|
k(t+c) = ln|T - 72|
T = 72 + Ae^kt, where A = ±e^c
When t = 0, T = 375,
A = 303
T = 303 e^kt
When T = 120,
kt = ln (120/303)
t = -(160ln (120/303))/303

Answer 2

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