Ice in a freezer is at $-7^{\circ} C .100 \,g$ of this ice is mixed with $200 \,g$ of water at $15^{\circ} C$. Take the freezing temperature of water to be $0^{\circ} C$, the specific heat of ice equal to $2.2 \,J / g { }^{\circ} C$, specific heat of water equal to $4.2 \,J / g ^{\circ} C$ and the latent heat of ice equal to $335 \,J / g$. Assuming no loss of heat to the environment, the mass of ice in the final mixture is closest to .......... $g$

A mass of material exists in its solid format its melting temperature $0\,^o  C$. The following processes then occur to the material

Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.

Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$

........ $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.

$1\, g$ of a steam at $100°C$ melt ........ $gm$ ice at $0°C\,?$ $($Latent heat of ice $= 80 \,cal/gm$ and latent heat of steam $= 540\, cal/gm)$

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 $= 540\, cal\, g^{-1}$]

$2\, kg$ 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 $80\, k\,cal/kg$ ........ $kg$

Ice at $-20\,^oC$ is added to $50\,g$ of water at $40\,^oC.$ When the temperature of the mixture reaches $0\,^oC,$ it is found that $20\,g$ of ice is still unmelted. The amount of ice added to the water was close to ........$g$ (Specific heat of water $= 4.2\,J/g/^oC)$ Heat of fusion of water at $0^oC = 334\,J/g$ )