Question

Question #adf2b

Answer 1

Linear expansion `alpha` is the length increase when an object is heated.
Volumetric expansion `gamma` is the volume increase.

Explanation:

If a block of material is heated, it will expand in all directions.

So in a block of `1mxx1mxx1m` with a linear coefficient of `alpha` the volume increases from `1m^3` to `(1+alpha)^3m^3` per degree.

Since `alpha` is very small (in the region of `10^(-5)//K`), we can say that `(1+alpha)^3~~1+3alpha` with sufficient precision.

So the co-efficient of volumetric expansion: `gamma~~3alpha`

Note:
`(1+alpha)^3=1+3alpha+3alpha^2+alpha^3` (Pascal)
Since `alpha` is very small (`~~10^-5`), `alpha^2` will be in the region of `10^(-10)` and `alpha^3~~10^(-15)`.
These can be neglected, hece `(1+alpha)^3~~1+3alpha`

Note 2:
Of course, with liquids you can only measure volume expansion.