In an experiment to find the liquid expansion coefficient $(\gamma)$,a column of experimental liquid at $T\,^oC$ is balanced against another column of experimental liquid at $0\,^oC$ by taking them in a $U$-tube. The expansion coefficient $(\gamma)$ is?

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):

The volume of a gas at $20^{\circ}C$ is $100 \, cm^3$ at normal pressure. If it is heated to $100^{\circ}C$,its volume becomes $125 \, cm^3$ at the same pressure,then the volume coefficient of the gas at normal pressure is:

$A$ 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

The value of the coefficient of volume expansion of glycerin is $5 \times 10^{-4} \ K^{-1}$. The fractional change in the density of glycerin for a rise of $40^{\circ}C$ in its temperature is:

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