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Math Help - Newtons Law of Cooling

  1. #1
    Member zangestu888's Avatar
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    Newtons Law of Cooling

    A cup of coffee was prepared at 90 degree C and left in a room at 20 degree C. Now the temperature is 60 degree and it is cooling at 1 degree/min. How much time has past since the coffee was made.
    ? netwons law ? dont know how to start it :S
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  2. #2
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    skeeter's Avatar
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    let y = temperature at any time t

    \frac{dy}{dt} = k(y - 20)

    at y = 60 degrees, \frac{dy}{dt} = -1 deg/min

    -1 = k(60 - 20)

    k = -\frac{1}{40}


    \frac{dy}{dt} = k(y - 20)

    separate variables and solve for y as a function of t ... you have k and you also know y(0) = 90
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  3. #3
    Member zangestu888's Avatar
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    thanks!

    thank you so very much for the help now i can conntiue!
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