$10 \,\,gm$ of ice at $0^o C$ is kept in a calorimeter of water equivalent $10 \,\,gm$. ……. $cal$ heat should be supplied to the apparatus to evaporate the water thus formed? (Neglect loss of heat)

An aluminium piece of mass $50 \,g$ initially at $300^{\circ} C$ is dipped quickly and taken out of $1 \,kg$ of water, initially at $30^{\circ} C$. If the temperature of the aluminium piece immediately after being taken out of the water is found to be $160^{\circ} C$, the temperature of the water ………… $^{\circ} C$ Then, specific heat capacities of aluminium and water are $900 \,Jkg ^{-1} K ^{-1}$ and $4200 \,Jkg ^{-1} K ^{-1}$, respectively.

In an industrial process $10\, kg$ of water per hour is to be heated from $20°C$ to $80°C$. To do this steam at $150°C$ 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 $90°C.$ how many $kg$ of steam is required per hour. $($Specific heat of steam $= 1$ $calorie \,per\, gm°C,$ Latent heat of vaporisation $= 540 \,cal/gm)$

In an experiment a sphere of aluminium of mass $0.20\, kg$ is heated upto $150\,^oC$. Immediately, it is put into water of volume $150\, cc$ at $27\,^oC$ kept in a calorimeter of water equivalent to $0.025\, kg$. Final temperature of the system is $40\,^oC$. The specific heat of aluminium is ………… $J/kg\,-\,^oC$ (take $4.2\, Joule= 1\, calorie$)

$50\, g$ ice at $0\,^oC$ is dropped into a calorimeter containing $100\, g$ water at $30\,^oC$. If thermal capacity of calorimeter is zero then amount of ice left in the mixture at equilibrium is …….. $gm$