Give the value of the coefficient of volume expansion at $0\,^{\circ}\text{C}$ for an ideal gas.

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 $100 \, ^\circ C$.

The coefficient of real expansion of mercury is $0.18 \times 10^{-3} \, ^{\circ}C^{-1}$. If the density of mercury at $0^{\circ}C$ is $13.6 \, g/cm^3$,what is its density at $473 \, K$?

$A$ glass flask is filled up to a mark with $50\, cc$ of mercury at $18^{\circ}C.$ If the flask and contents are heated to $38^{\circ}C,$ how much mercury will be above the mark? (Given: $\alpha$ for glass is $9 \times 10^{-6} {^{\circ}C}^{-1}$ and the coefficient of real expansion of mercury is $180 \times 10^{-6} {^{\circ}C}^{-1}$)

$A$ glass flask of volume $1 \, L$ is completely filled with mercury at $0 \, ^\circ C$. The temperature of the glass flask and mercury is raised to $100 \, ^\circ C$. If the coefficient of volume expansion of mercury is $1.82 \times 10^{-4} \, ^\circ C^{-1}$ and the coefficient of linear expansion of glass is $0.1 \times 10^{-4} \, ^\circ C^{-1}$,how much mercury will overflow from the flask? (in $cm^3$)

What is $\alpha_V$? On what value of $\alpha_V$ depends? Write its unit.