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Math Help - Newton's Law of Cooling

  1. #1
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    Newton's Law of Cooling

    Hi everyone, thanks for taking the time to help me out!

    Question: An object of temperature 120 degree F is placed in a medium maintained at a constant temperature m degree F. At the end of 2 minutes the temperature of the object is 90 degree F and after another 2 minutes its temperature is 72 degree F.

    (i) Find m
    (ii) When will the temperature of the object be 61.20 degree F?
    (iii) What is the temperature of the object at the end of 8 minutes?


    (i) T(t)=Ta+(To-Ta)e^-kt
    I know that Ta=90 F, To can be 120 degree F when T(2)=90 and t=2. I still have two unknowns left and i cant solve for Ta, so i need help here.

    T(2)=90=Ta+(120-90)e^-2t

    As for the rest if i can get the equation i will be able to solve!
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  2. #2
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    At T(0)=120.

    By \frac{dt}{T-m}=kdt

    Integrate both sides gives:

    ln(T-m)=kt+C

    T=e^{kt+C}+m

    T=Ke^{kt}+m

    At T(0) we have T=120

    120=Ke^{kt}+m......[1]

    At T(2) we have 90:

    90=Ke^{2k}+m....[2]

    At T(4) we have 72:

    72=Ke^{kt}+m....[3]

    We have three equations to solve, [1], [2], and [3].

    From [1], K=120-m

    Sub into [2] and get

    90=(120-m)e^{2k}+m

    Can you finish?.
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  3. #3
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    I'm not exactly sure where to go from here after ive substituted into the equation. I still have m and k left.
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