Newton's Law of Cooling?
A pie is removed from a 375 degree oven and cools to 215 degrees after 15 minutes in a room at 72 degrees F. How long from the time it is removed from the oven will it take the pie to cool to 120 degrees F using Newton’s Law of Cooling.
- BryceLv 71 month ago
dT/dt= k(T - Tm), Tm= the temperature of the surrounding medium
dT/(T - Tm)= kdt
ln|T - Tm|= kt + C
T - Tm= ce^(kt)
At t= 0, 375 - 72=c; c= 303
At t= 15, 215 - 72= 303e^(15k); k≈ -0.05006
T(t)= 303e^(-0.05006t) + 72
120 - 72= 303e^(-0.05006t)
ln(0.158415...)= -0.05006t; t≈ 36.8 min