Question #adf2b

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Question #adf2b

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Answer 1 · 2017-03-18T14:35:37

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.

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