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Volumetric expansion

  1. Nov 23, 2009 #1
    Hello, Could someone explain to me when referring to temperature and heat, speciffically volume thermal expansion how 3 alpha equals beta? If you could show me in a formula that would be great!
     
  2. jcsd
  3. Nov 23, 2009 #2

    Mapes

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    Hi mjongem, welcome to PF. The approximation [itex]\beta=3\alpha[/itex] is something you can prove to yourself.

    1. Start with the definitions of linear and volumetric thermal expansion coefficiencts.
    2. Considering a cube, write the volume change as a function of unit volume in terms of [itex]\alpha[/itex] and [itex]\beta[/itex].
    3. Assume small expansions compared to the size of the object, and simplify power terms by a Taylor series expansion (e.g., [itex](1+a)^3\approx 1+3a[/itex] when a is small).
     
  4. Nov 23, 2009 #3
    I was wondering if you would show me the exact wat to derive my question, I have not taken calculus before, and I just wanted to see how three alpha equals beta
     
  5. Nov 23, 2009 #4

    Mapes

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    We don't just provide solutions here, since that wouldn't help anyone learn. If you show your work in solving a problem, though, you'll usually be able to get help if you get stuck.

    If you're interested in solving the problem yourself, try the steps I outlined above. Calculus isn't necessary once you have the approximation [itex](1+\alpha)^3\approx 1+3\alpha[/itex].
     
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