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Q.
If the coefficient of cubical expansion is $ x $ times of the coefficient of superficial expansion, then value of $ x $ is:
Jharkhand CECEJharkhand CECE 2003
Solution:
The linear expansivity of a solid is also referred to as the thermal coefficient of linear expansion, and is frequently given the symbol $(\alpha)$.
As solids expand, so does their surface areas and volumes.
The terms superficial expansivity $(\beta)$ or thermal coefficient of superficial expansion is used when describing area changes due to temperature changes.
For volume changes, the term cubic expansivity $(\gamma)$ or thermal coefficient of cubic expansion is used.
For most solids, the relationships $\gamma=3 \alpha$ and $\beta=2 \alpha$ hold.
Hence, we have $\gamma=\frac{3 \beta}{2}=1.5 \beta$
$\Rightarrow x \beta=1.5 \beta $
$(\because \gamma=x \beta)$
Hence, value of $x$ is $1.5$.