Question

The relation between the coefficient of real expansion $\left(\gamma_{r}\right)$ and coefficient of apparent expansion $\left(\gamma_{a}\right.$ ) of a liquid and the coefficient of linear expansion $\left(\alpha_{g}\right)$ of the material of the container is

• A. $\gamma_{r}=\alpha_{g}+\gamma_{a}$
• B. $\gamma_{r}=\alpha_{g}+3 \gamma_{a}$
• C. $\gamma_{r}=3 \alpha_{g}+\gamma_{a}$
• D. $\gamma_{r}=3\left(\alpha_{g}+\gamma_{a}\right)$

Answer 1

Answer: (C)

Coefficient of real expansion
$=$ coefficient of apparent expansion $+$ coefficient of expansion of material of container
$\gamma_{r}=\gamma_{a}+\gamma_{g}$
but $\gamma=3 \alpha$
So, $\gamma_{g}=3 \alpha_{g}$
$\therefore \gamma_{r}=\gamma_{a}+3 \alpha_{g}$