The apparent coefficient of expansion of a liquid when heated in a brass vessel is $X$ and when heated in a tin vessel is $Y$. If $\alpha$ is the coefficient of linear expansion for brass, the coefficient of linear expansion of tin is ..........

$A$ beaker is completely filled with water at $4^{\circ}C$. It will overflow if

$A$ glass flask of volume $1 \ L$ 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 $cc$)

When a liquid is heated in a copper vessel, its coefficient of apparent expansion is $6 \times 10^{-6} /{ }^{\circ} C$. When the same liquid is heated in a steel vessel, its coefficient of apparent expansion is $24 \times 10^{-6} /{ }^{\circ} C$. If the coefficient of linear expansion for copper is $18 \times 10^{-6} /{ }^{\circ} C$, find the coefficient of linear expansion for steel.

The density of water at $20^oC$ is $0.998 \, g/cm^3$ and at $40^oC$ is $0.992 \, g/cm^3$. The mean coefficient of cubical expansion (in per $^oC$) is:

The densities of a liquid at $0^{\circ} C$ and $100^{\circ} C$ are respectively $1.0127 \ g/cm^3$ and $1 \ g/cm^3$. $A$ specific gravity bottle is filled with $300 \ g$ of the liquid at $0^{\circ} C$ up to the brim and it is heated to $100^{\circ} C$. Then,the mass of the liquid expelled in grams is: (Coefficient of linear expansion of glass $= 9 \times 10^{-6} /^{\circ} C$)