The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \, K^{-1}$. The fractional change in the density on a $30^{\circ} C$ rise in temperature is ..........

The relation between the coefficient of real expansion $(\gamma_r)$ and coefficient of apparent expansion $(\gamma_a)$ of a liquid and the coefficient of linear expansion $(\alpha_g)$ of the material of the container is:

$A$ glass vessel of volume $V_0$ is completely filled with a liquid and its temperature is raised by $\Delta T$. What volume of the liquid will flow over,if the coefficient of linear expansion of glass is $\alpha_g$ and the coefficient of volume expansion of the liquid is $\gamma_L$?

The coefficient of apparent expansion of mercury in a glass vessel is $132 \times 10^{-6} /^{\circ}C$ and in a steel vessel is $114 \times 10^{-6} /^{\circ}C$. If $\alpha$ for steel is $12 \times 10^{-6} /^{\circ}C$,then that of glass is:

Give the value of the coefficient of volume expansion at room temperature for an ideal gas.

"Anomalous expansion of water is a blessing for living organisms in water." Explain this statement. Explain the anomalous expansion of water.