Question

The relation between the coefficient of real expansion $\left({\gamma }_r\right)$ and coefficient of apparent expansion $({\gamma }_a$ ) 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, ${\gamma }_g=3{\alpha }_g$
$\therefore {\gamma }_r={\gamma }_a+3{\alpha }_g$