$A$ block of ice at $-20\,^oC$ having a mass of $2\,kg$ is added to $3\,kg$ of water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container,what is the final state of the system?

$5\,g$ of ice at $0\,^{\circ}C$ is dropped in a beaker containing $20\,g$ of water at $40\,^{\circ}C$. The final temperature will be ........ $^{\circ}C$.

$A$ calorimeter contains $0.2 \ kg$ of water at $30^{\circ}C$. When $0.1 \ kg$ of water at $60^{\circ}C$ is added to it,the final temperature of the mixture becomes $35^{\circ}C$. What is the heat capacity of the calorimeter in $J/K$?

$100 \, g$ of ice at $0^{\circ}C$ is mixed with $100 \, g$ of water at $100^{\circ}C$. What will be the final temperature of the mixture in $^{\circ}C$?

$300 \text{ g}$ of water at $25^{\circ}C$ is added to $100 \text{ g}$ of ice at $0^{\circ}C$. The final temperature of the mixture is (in $^{\circ}C$)

The water equivalent of a calorimeter is $10 \ g$ and it contains $50 \ g$ of water at $15^{\circ} C$. Some amount of ice, initially at $-10^{\circ} C$, is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was dropped (given specific heat of ice $= 0.5 \ cal \ g^{-1} {}^{\circ} C^{-1}$, specific heat of water $= 1.0 \ cal \ g^{-1} {}^{\circ} C^{-1}$ and latent heat of melting of ice $= 80 \ cal \ g^{-1}$) (in $g$)?