Question

The coefficient of volume expansion is :

• A. twice the coefficient of linear expansion
• B. twice the coefficient of real expansion
• C. thrice the coefficient of real expansion
• D. thrice the coefficient of linear expansion

Answer 1

The correct option is D thrice the coefficient of linear expansion

If we consider $\alpha$ and $\gamma$ as the linear and volumetric expansion then linear expansion is given by
$L\to L(1+\alpha \Delta T)$
Similarly,
$V\to V(1+\gamma \Delta T)$.
Also, $V=L^3$
$⟹V=L^3(1+\alpha \Delta T{)}^3$
$=L^3(1+3\alpha \Delta T+{\alpha }^2\Delta T^2+{\alpha }^3\Delta T^3)$
Since the thermal expansion coefficient is of the order of parts per million per ${}^{o}C$, we can neglect quadratic and cubic terms.
Hence, $⟹V=L^3(1+3\alpha \Delta T)$
$⟹\gamma =3\alpha$