A vessel contains $110\, g$ of water. The heat capacity of the vessel is equal to $10\, g$ of water. The initial temperature of water in vessel is $10°C.$ If $220\, g$ of hot water at $70°C$ is poured in the vessel, the final temperature neglecting radiation loss, will be........ $^oC$

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.

$2\  kg$ ice at $-20^o\ C$ is mixed with $5\  kg$ water at $20^o\ C$. Then final amount of water in the mixture would be ; Given specific heat of ice $= 0.5\ cal/g^o\ C$, specific heat of water $= 1\  cal/g^o\ C$, Latent heat of fusion of ice $= 80\  cal/g$ ........ $kg$

$10 \,\,gm$ 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)

Calorie is defined as the amount of heat required to raise temperature of $1g$ of water by $1°C$ and it is defined under which of the following conditions

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