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I was trying to derive the formula that the coefficient for volume expansion, β, is 3 times the coefficient for length expansion, [itex]\alpha[/itex].

As a reminder, the formulas are:

[itex]\Delta[/itex]L = [itex]\alpha[/itex]L

_{o}[itex]\Delta[/itex]T

and [itex]\Delta[/itex]V = [itex]\beta[/itex]V

_{o}[itex]\Delta[/itex]T

where, supposedly, [itex]\beta[/itex] = 3[itex]\alpha[/itex].

My proof actually gave me a completely different result. I double-checked it a few times, and I can't find the problem. Does anyone know what's wrong?

here it is: http://imageshack.us/photo/my-images/267/img20111212204020.jpg/

thanks in advance,

doublefelix92