$1 \,kg$ of ice at $-20^{\circ} C$ is mixed with $2 \,kg$ of water at $90^{\circ} C$. Assuming that there is no loss of energy to the environment, the final temperature of the mixture is ............ $^{\circ} C$ (Assume, latent heat of ice $=334.4 \,kJ / kg$, specific heat of water and ice are $4.18 \,kJ kg ^{-1} K ^{-1}$ and $2.09 \,kJ kg ^{-1}- K ^{-1}$, respectively.)

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 $540^{\circ} C$

A metal bal of mass $0.1\, kg$ is heated upto $500\,{}^oC$ and dropped into a vessel of heat capacity $800\, JK^{-1}$ and containing $0.5\, kg$ water. The initial temperature of water and vessel is $30\,{}^oC$. ........ $\%$ is the approximate percentage increment in the temperature of the water. [Specific heat Capacities of water and metal are, respectively $4200\, Jkg^{-1}K^{-1}$ and $400\, Jkg^{-1}K^{-1}$]

One end of a $2.35\,\,m$ long and $2.0\,\,cm$ radius aluminium rod$(K = 235 \,\,W.m^{-1}K^{-1})$ is held at $20^0\,\,C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg.s^{-1}$ at which ice melts is

[Take latent heat of fusion for ice as $\frac{{10}}{3} ×10^5 J.kg^{-1} $]

Calorimeters are made of which of the following

Work done in converting $1\, g$ of ice at $-10\,^oC$ into steam at $100\,^oC$ is ......... $J$