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Total energy required

  1. Jun 10, 2010 #1
    Hi,

    a question at work popped up and it's been too long since I went to school :p

    The total energy [Wh] required to heat the system to temperature T is given by f(T)=1.28T. The effect [W] applied to the system is given by g(T)=378-3.16T. How long does it take to heat the material to say 80 degrees?

    Hope someone can help me out, thanks.
     
  2. jcsd
  3. Jun 10, 2010 #2
    Here's my try. I'm using wolframalpha for the differentiation and integration...


    [tex]
    \frac{dh}{dT}=\frac{d}{dT}\left(\frac{f(T)}{g(T)}\right)
    [/tex]

    [tex] =\frac{d}{dT}\left(\frac{1.28T}{378-3.16T}\right) [/tex]

    [tex]=\frac{4.04T}{(378-3.16T)^2}+\frac{1.28}{378-3.16T} [/tex]

    So now I have the change in time required to heat up the material as a function of temperature. I integrate to get the time required:

    [tex] h(T)=\frac{153.1}{378-3.16T} [/tex]

    Meh, at least it's an attempt :p
     
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