Steam at $100\,^oC$ is passed into $20\, g$ of water at $10\,^oC$. When water acquires a temperature of $80\,^oC$, the mass of water present will be …….. $g$

[Take specific heat of water $= 1\, cal\, g^{-1}\,^oC^{-1}$ and latent heat of steam $= 540\, cal\, g^{-1}$]

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

Heat is being supplied at a constant rate to the sphere of ice which is melting at the rate of $0.1 \,gm / s$. It melts completely in $100 \,s$. The rate of rise of temperature thereafter will be ………… $^{\circ} C / s$

$300\, gm$ of water at $25°C$ is added to $100\, gm$ of ice at $0°C$. The final temperature of the mixture is…….. $^oC$

The relative humidity on a day, when partial pressure of water vapour is $0.012 \times {10^5}\,Pa$ at $12°C$ is ……… $\%$ (take vapour pressure of water at this temperature as $0.016 \times {10^5}\,Pa$)