Volume Expansion

Volume expansion:

V = L³ = L₀³(1+aDT)³ = V₀(1+3aDT+...) => DV/V = 3aDT

You could also write a formula with the coefficient of volume expansion, g, as:

DV/V = gDT

Comparing the last two formulas then yields:

g = 3a

In both of the above derivations we were able to neglect terms higher than linear in a, because a is so small => aDT « 1

Please note: You need to be careful here. If you want to calculate the volume expansion and you are given the coefficient of linear expansion, a, then the formula you need to use is:

DV = 3aDT V

If, however, you are given the coefficient of volume expansion, g, then the formula you need to use is:

DV = g DT V

The factor of 3 that these differ by can cause confusion, if one is not careful.