A piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $h$ is

[Latent heat of ice is $3.4 \times 10^{5}\; J / k g$ and $g=10\; N / kg ]$

A tap supplies water at $10\,^oC$ and another tap at $100\,^oC$. ………. $kg$ hot water must be taken so that we get $20\, kg$ water at $35\,^oC$ ?

$100\,g$ of water is supercooled to $-\,10\,^oC$. At this point, due to some disturbance mechanised or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze ? $[S_W = 1\,cal\,g^{-1}\,^oC^{-1}$ and ${L^W}_{{\text{fussion}}}$ $= 80\,cal\,g^{-1}]$

An earthen pitcher used in summer cools water in it essentially by evaporation of water from its porous surface. If a pitcher carries $4 \,kg$ of water and the rate of evaporation is $20$ g per hour, temperature of water in it decreases by $\Delta T$ in two hours. The value of $\Delta T$ is close to ……….. $^{\circ} C$ (ratio of latent of evaporation to specific heat of water is $540^{\circ} C$

$100 \,gm$ of ice at $0°C$ is mixed with $100\, g$ of water at $100°C.$ What will be the final temperature of the mixture ………. $^oC$