Heat needed to convert $1$ kilogram ice at $0^o\,C$ to steam at $100^o\,C$ is

A block of ice at $-20\,^oC$ having a mass of $2\, kg$ is added to a $3\, kg$ water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container

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

A thermally insulated vessel contains some water at $0^0C$. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given Latent heat of vaporization of water at $0^o C =21 × 10^5 J/kg$ and latent heat of freezing of water $= 3.36 × 10^5 J/kg$. The maximum percentage amount of water that will be solidified in this manner will be ...... $\%$

Two liquids $A$ and $B$ are at $32\,^oC$ and $24\,^oC.$ When mixed in equal masses the temperature of the mixture is found to be $28\,^oC$. Their specific heats are in the ratio of

Steam at $100°C$ is passed into $1.1\, kg$ of water contained in a calorimeter of water equivalent $0.02 \,kg$ at $15°C$ till the temperature of the calorimeter and its contents rises to $80°C.$ The mass of the steam condensed in $kg$ is