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Thread: Temperature of a conductor equation

  1. #1
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    Temperature of a conductor equation

    If anyone can help me out with this it will be much appreciated.

    The temperature of a conductor at time, t, is given by:



    Where is the initial temperature and T is a constant

    Express T in terms of , , and t and determine its value when = 190, = 20 and t = 40.
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  2. #2
    MHF Contributor

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    This doesn't really belong in "Linear and Abstract Algebra", it is just a matter of basic algebra.

    From $\displaystyle \theta= \theta_0\left(1- e^{\frac{t}{T}}\right)$ you can divide both sides by $\displaystyle \theta_0$ to get $\displaystyle \frac{\theta}{\theta_0}= 1- e^{\frac{t}{T}}$. Now add $\displaystyle e^{\frac{t}{T}}$ to both sides and subtract $\displaystyle \frac{\theta}{\theta_0}$ from both sides to get $\displaystyle e^{\frac{t}{T}}= 1- \frac{\theta}{\theta_0}$

    Take the natural logarithm of both sides to get
    $\displaystyle \frac{t}{T}= ln\left(1- \frac{\theta}{\theta_0}\right)$

    Can you finish it from there?
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  3. #3
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    Yes I can, thank you.
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