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Math Help - need help...forgotten the basics

  1. #1
    hks
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    need help...forgotten the basics

    i am trying to solve this [t is time and T is temperature] to find the time t,

    6450*Pi*(0.00185^2)*(0.0625)*836
    dt = --------------------------------------------- dT
    (1.2^2)*7.5 - 108*Pi*0.00185*0.25*T

    between the limits 0 and 180degC

    i have tried & got this answer, t = 3.6236 ln (10.8 - 0.156923*T)

    and when solving between the limits, I am getting error because of ln (10.8-0.156923(180)) which is negative.

    can someone help me
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  2. #2
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    Your equation is a mess. Type it more neatly.
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  3. #3
    hks
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    sorry, hope this is more readable

    dt = (3.6236)/(10.8 - 0.156923T) dT

    thanks
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  4. #4
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    Quote Originally Posted by hks View Post
    sorry, hope this is more readable

    dt = (3.6236)/(10.8 - 0.156923T) dT

    thanks
    Ignore the numbers,
    Say, a,b,c>0 and we have:

    dt = \frac{a}{b-c\tau }d\tau

    I hate the subhuman differencial notation, let me write instead,

    \frac{dt}{d\tau}=t' = \frac{a}{b-c\tau}

    Now integrate both sides,

    \int t' d\tau = \int \frac{a}{b-c\tau} d\tau

    t = -\frac{a}{c}\ln |b-c\tau|+C

    Now just evaluate this at \tau = 180 and then subtract \tau =0. (You can ignore the constant).

    Once you do that you can substitute the true values for a,b,c.
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