How many grams of ice at $0 \, ^\circ \text{C}$ will be melted by $1 \, \text{g}$ of steam at $100 \, ^\circ \text{C}$? (Latent heat of fusion of ice $L = 80 \, \text{cal/g}$ and latent heat of vaporization of water $L' = 540 \, \text{cal/g}$)

In an industrial process,$10 \, kg$ of water per hour is to be heated from $20^\circ C$ to $80^\circ C$. To do this,steam at $150^\circ C$ is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at $90^\circ C$. How many $kg$ of steam is required per hour? (Specific heat of steam $= 1 \, cal/g^\circ C$,Latent heat of vaporisation $= 540 \, cal/g$)

If equal masses of $10$ liquids of specific heats $s, 2s, 3s, \ldots, 10s$ at temperatures $10^{\circ} C, 20^{\circ} C, 30^{\circ} C, \ldots, 100^{\circ} C$ respectively are mixed,the resultant temperature of the mixture is . . . . . . . (in $^{\circ} C$)

Steam at $100^{\circ}C$ is added slowly to $1400 \, \text{g}$ of water at $16^{\circ}C$ until the temperature of the water is raised to $80^{\circ}C$. The mass of steam required to do this is $(L_V = 540 \, \text{cal/g})$ ........... $\text{g}$

Objects $A$ and $B$ that are initially separated from each other and well isolated from their surroundings are then brought into thermal contact. Initially $T_A = 0^{\circ}C$ and $T_B = 100^{\circ}C$. The specific heat of $A$ is less than the specific heat of $B$. After some time,the system comes to an equilibrium state. The final temperatures are :

$5 \ g$ of ice at $-30^{\circ} C$ and $20 \ g$ of water at $35^{\circ} C$ are mixed together in a calorimeter. The final temperature of the mixture is (Neglect heat capacity of the calorimeter,specific heat capacity of ice $= 0.5 \ cal \ g^{-1} {}^{\circ} C^{-1}$,latent heat of fusion of ice $= 80 \ cal \ g^{-1}$,and specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$). (in $^{\circ} C$)