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

If $\alpha_V$ and $T$ are the coefficient of volume expansion and temperature for an ideal gas respectively, then

Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at $0^{\circ}C$ while the tube on the right is kept at $30^{\circ}C$ in a water bath. The difference in the levels of the liquid in the two tubes is $4 \, cm$ while the height of the liquid column at $0^{\circ}C$ is $120 \, cm$. The coefficient of volume expansion of the liquid is (Ignore expansion of the glass tube):

In a vertical $U-$tube containing a liquid,the two arms are maintained at different temperatures ${t_1}$ and ${t_2}$. The liquid columns in the two arms have heights ${l_1}$ and ${l_2}$ respectively. The coefficient of volume expansion of the liquid is equal to

$A$ liquid having a coefficient of cubical expansion $\gamma$ is kept in a copper vessel having a coefficient of linear expansion $\alpha = \frac{\gamma}{3}$. If heat is supplied to the vessel,the original level of the liquid in the vessel will

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