Find the amount of heat supplied to decrease the volume of an ice-water mixture by $1 \, cm^3$ without any change in temperature. (Given: $\rho_{ice} = 0.9 \rho_{water}$,$L_{ice} = 80 \, cal/g$).

The heat required to convert $8 \ g$ of ice at a temperature of $-20^{\circ}C$ to steam at $100^{\circ}C$ is (Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$, specific heat capacity of water $= 4200 \ J \ kg^{-1} \ K^{-1}$, latent heat of fusion of ice $= 336 \times 10^3 \ J \ kg^{-1}$ and latent heat of steam $= 2.268 \times 10^6 \ J \ kg^{-1}$) (in $kJ$)

The heat extracted out of $x \ \text{g}$ of water initially at $50^\circ \text{C}$ to cool it down to $0^\circ \text{C}$ is sufficient to evaporate $(1000 - x) \ \text{g}$ of water also initially at $50^\circ \text{C}$. The value of $x$ (closest integer) is . . . . . . . (Take latent heat of water $L = 2256 \ \text{kJ/kg}$, specific heat capacity of water $c = 4200 \ \text{J/kg}\cdot \text{K}$)

$A$ beaker is completely filled with water at $4 \text{ } ^\circ C$. When will the water in this beaker overflow?

The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is $1 : 4$. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?

Work done in converting one gram of ice at $-10^{\circ}C$ into steam at $100^{\circ}C$ is ....... $J$