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} $]

Heat given to a body which raises its temperature by $1\ ^oC$ is

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 $=2.256 \times 10^{6}\; J \,kg ^{-1}$

$50 \,g$ ice at $0^{\circ} C$ is dropped into a calorimeter containing $100 \,g$ water at $30^{\circ} C$. If thermal capacity of calorimeter is zero then amount of ice left in the mixture at equilibrium is ………. $g$

Due to cold weather a $1\, {m}$ water pipe of cross-sectional area $1\, {cm}^{2}$ is filled with ice at $-10^{\circ} {C}$. Resistive heating is used to melt the ice. Current of $0.5\, {A}$ is passed through $4\, {k} \Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In ${s}$)

(Given latent heat of fusion for water/ice $=3.33 \times 10^{5}\, {J} {kg}^{-1}$, specific heat of ice $=2 \times 10^{3}\, {J}$ ${kg}^{-1}$ and density of ice $=10^{3}\, {kg} / {m}^{3}$