Find the difference in temperature between the water at the top and the bottom of a $20 \ m$ high waterfall, assuming $10 \%$ of the energy of the fall is spent in heating the water. [Use specific heat capacity of water $= 4000 \ J \ kg^{-1} K^{-1}$ and $g = 10 \ m/s^2$]. (in $^{\circ} C$)

$500\, g$ of water and $100\, g$ of ice at $0\,^{\circ}C$ are in a calorimeter whose water equivalent is $40\, g$. $10\, g$ of steam at $100\,^{\circ}C$ is added to it. Then the final amount of water in the calorimeter is ....... $g$ (Latent heat of ice $= 80\, cal/g$,Latent heat of steam $= 540\, cal/g$).

$ 1 \text{ g} $ of ice is mixed with $ 1 \text{ g} $ of steam. At thermal equilibrium,the temperature of the mixture is (in $^{\circ} C$)

The amount of heat needed to heat $200 \ g$ of ice at $-10^{\circ}C$ to convert it into water at $30^{\circ}C$ is:
Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$
Specific heat capacity of water $= 4186 \ J \ kg^{-1} \ K^{-1}$
Latent heat of fusion of ice $= 3.35 \times 10^5 \ J \ kg^{-1}$ (in $J$)

Calculate the heat required to convert $3 \; kg$ of ice at $-12 \; ^{\circ}C$ kept in a calorimeter to steam at $100 \; ^{\circ}C$ at atmospheric pressure. Given: specific heat capacity of ice $= 2100 \; J \; kg^{-1} \; K^{-1}$,specific heat capacity of water $= 4186 \; J \; kg^{-1} \; K^{-1}$,latent heat of fusion of ice $= 3.35 \times 10^{5} \; J \; kg^{-1}$,and latent heat of steam $= 2.256 \times 10^{6} \; J \; kg^{-1}$.

$A$ drilling machine of $10 \, kW$ power is used to drill a bore in a small aluminium block of mass $8 \, kg$. If $50 \%$ of power is used up in heating the machine itself or lost to the surroundings,then the rise in temperature of the block in $2.5 \, minutes$ is ........ $^\circ C$. [Specific heat of aluminium $= 0.91 \, J/g \cdot ^\circ C$]