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I am being asked to show an equation (a) for thermal expansion is equivalent to another equation (b).

Show that the following equation for thermal expansion enter image description here is equivalent to enter image description here

I have never come across this type of question before.

What am I being asked to demonstrate in answering the question and how might I start? If there are examples I can be pointed towards, that would be appreciated. Note that I'm not necessarily asking for anybody to do my work for me!

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    If in fact your book has defined/stated that $\Delta X=X-X_0$ to begin with, then the proof is not terribly difficult...2012-02-09

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Because $\Delta X = X - X_0$ as specified, it is a simple algebraic manipulation to show equivalence:

$X = X_0(1 + \alpha \Delta T) = X_0 + X_0\alpha\Delta T$

Subtract $X_0$ from both sides to get:

$\Delta X = X - X_0 = X_0\alpha\Delta T$

This all falls back on basic algebra. The reason you may be asked to prove such an equivalence is just to clarify that the same formula can be expressed in several ways, and when using such a formula you can choose a form which is most conducive to your data (or the problem space).

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    Hi Kurtis. That's the question as it appears. I honestly don't know what it's expecting me to show. I imagined perhaps a step-by-step approach, but that was assuming that the answer required would have looked a bit more complex than that. It would be reasonable to assume that what you've offered there is probably what I'm expected to set out. Thanks for your help.2012-02-09