$A$ gas at $20 \, ^\circ C$ and normal pressure has a volume of $100 \, cm^3$. If its temperature is increased to $100 \, ^\circ C$ at the same pressure,its volume becomes $125 \, cm^3$. Calculate the coefficient of volume expansion of the gas at normal pressure in $^\circ C^{-1}$.

$A$ 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

$A$ bakelite beaker has a volume capacity of $500\, cc$ at $30^{\circ} C$. When it is partially filled with $V_{m}$ volume (at $30^{\circ} C$) of mercury,it is found that the unfilled volume of the beaker remains constant as the temperature is varied. If $\gamma_{\text{beaker}} = 6 \times 10^{-6}{ }^{\circ} C^{-1}$ and $\gamma_{\text{mercury}} = 1.5 \times 10^{-4}{ }^{\circ} C^{-1}$,where $\gamma$ is the coefficient of volume expansion,then $V_{m}$ (in $cc$) is close to

The coefficients of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$, respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$, the coefficient of linear expansion of the vessel $B$ is

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:

The relation between the coefficient of real expansion $(\gamma_r)$ and coefficient of apparent expansion $(\gamma_a)$ of a liquid and the coefficient of linear expansion $(\alpha_g)$ of the material of the container is: