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.

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  • Bryce
    Lv 7
    1 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)

    0.158415...= e^(-0.05006t)

    ln(0.158415...)= -0.05006t; t≈ 36.8 min

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