Question

If the coefficient of cubical expansion is $x$ times of the coefficient of superficial expansion, then value of $x$ is:

• A. 2.7
• B. 2
• C. 1.5
• D. 9.5

Answer 1

Answer: (C)

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 $1.5$.