Work done in converting one gram of ice at $-10°C$ into steam at $100°C$ is ....... $J$

The specific heat of a metal at low temperatures varies according to $S = aT^3$ where a is a constant and $T$ is the absolute temperature. The heat energy needed to raise unit mass of the metal from $T = 1 K$ to $T = 2 K$ is

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 $=10^{3}\, {kg} / {m}^{3}$

$2\, kg$ of ice at $-20°C$ is mixed with $5\, kg$ of water at $20°C$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $1\, kcal/kg\, per °C$ and $0.5\, kcal/kg/°C$ while the latent heat of fusion of ice is $80\, k\,cal/kg$ ........ $kg$

$80\, gm$ of water at $30°C$ are poured on a large block of ice at $0°C.$ The mass of ice that melts is ........ $gm$

Compared to a burn due to water at $100°C$, a burn due to steam at $100°C$ is