$5 \, g$ of ice at $0^{\circ}C$ is mixed with $5 \, g$ of steam at $100^{\circ}C$. The final temperature of the mixture is ... $^{\circ}C$.

$A$ beaker of height $H$ is made up of a material whose coefficient of linear thermal expansion is $3\alpha$. It is filled up to the brim by a liquid whose coefficient of thermal expansion is $\alpha$. If now the beaker along with its contents is uniformly heated through a small temperature $T$,the level of liquid will reduce by (given $\alpha T << 1$):

By exerting a certain amount of pressure on an ice block,you:

Consider a rectangular sheet of solid material of length $l=9 \ cm$ and width $d=4 \ cm$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \ K^{-1}$ at room temperature and one atmospheric pressure. The mass of the sheet is $m=0.1 \ kg$ and the specific heat capacity is $C_v=900 \ J \ kg^{-1} K^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \ J$,then the change in area of the rectangular sheet is:

The surface of the lake is at $2^{\circ} C$. The temperature of the bottom of the lake is ....... $^{\circ} C$.

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 $c = 4200 \ \text{J/kg}\cdot \text{K}$)