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 $40 \, ^oC$ in its temperature is:

What is volume expansion? Give the definition and unit of the coefficient of volume expansion.

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 coefficient of volumetric expansion of mercury is $18 \times 10^{-5} \, ^\circ C^{-1}$. $A$ thermometer bulb has a volume $10^{-6} \, m^3$ and the cross-section of the stem is $0.004 \, cm^2$. Assuming that the bulb is filled with mercury at $0 \, ^\circ C$,find the length of the mercury column at $100 \, ^\circ C$.

$A$ liquid with a coefficient of volume expansion $\gamma$ is filled in a container of a material having a coefficient of linear expansion $\alpha$. If the liquid overflows on heating,then

$A$ glass flask of volume $1 \text{ litre}$ is filled completely with mercury at $0^{\circ} C$. The flask is now heated to $100^{\circ} C$. The coefficient of volume expansion of mercury is $1.82 \times 10^{-4} /{ }^{\circ} C$ and the coefficient of linear expansion of glass is $0.1 \times 10^{-4} /{ }^{\circ} C$. During this process, the amount of mercury which overflows is (in $\text{ cc}$)