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Math Help - upper o lower vaule for the constant, k in newt law cooling

  1. #1
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    Cool upper o lower vaule for the constant, k in newt law cooling

    I have asked a similar question before but i realised i was asking the wrong thing...........

    a. for the equation dT/dt= -k(T-8) what is the upper or lower limit of k if the temperature (T) is to never fall below T=15 ......... when t=0, T=16

    b. if k=0 what does this say about the insulation properties of k?

    THANK YOU!!!!!!!!!!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by zena View Post
    I have asked a similar question before but i realised i was asking the wrong thing...........

    a. for the equation dT/dt= -k(T-8) what is the upper or lower limit of k if the temperature (T) is to never fall below T=15 ......... when t=0, T=16

    b. if k=0 what does this say about the insulation properties of k?

    THANK YOU!!!!!!!!!!!
    Post clarifications in the same thread as your original equation, where part (b) has already been answered
    if I recall correctly.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by zena View Post
    I have asked a similar question before but i realised i was asking the wrong thing...........

    a. for the equation dT/dt= -k(T-8) what is the upper or lower limit of k if the temperature (T) is to never fall below T=15 ......... when t=0, T=16

    b. if k=0 what does this say about the insulation properties of k?

    THANK YOU!!!!!!!!!!!
    First solve the differential equation.

    In this case the solution is:

    <br />
T=8(1+e^{-kt})<br />

    so when t=0,\ T=16, and if k>0 as t \to \infty\ T \to 8.

    Hence for all k>0 the temprature eventualy drops below 15.
    If k \le 0 the temprature never falls below 16.

    RonL
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