$10 \, g$ of ice at $0^{\circ}C$ is mixed with $100 \, g$ of water at $50^{\circ}C$. What is the resultant temperature of the mixture in $^{\circ}C$?

$A$ $10 \,kW$ drilling machine is used to drill a bore in an aluminium block of mass $25 \,kg$. If the machine is on for $3 \,minutes$ and $50 \%$ of the heat liberated is absorbed by the block, what is the rise in temperature of the block (in $^{\circ} C$)? (Specific heat of aluminium is $900 \,J \,kg^{-1} \,K^{-1}$)

$15 \text{ g}$ of ice at $0^{\circ}\text{C}$ is added to a vessel containing water at $40^{\circ}\text{C}$. The mass of water and water equivalent of the vessel is $60 \text{ g}$. Assuming that negligible heat is taken from the surroundings, the final temperature of the mixture will be $[L_{\text{ice}} = 80 \text{ cal/g}, S_{\text{water}} = 1 \text{ cal/g}]$ (in $^{\circ}\text{C}$)

$A$ block of mass $2.5 \ kg$ is heated to a temperature of $500^{\circ} C$ and placed on a large ice block. What is the maximum amount of ice (in $kg$) that can melt (approx.)? (Specific heat of the body $= 0.1 \ cal/g^{\circ} C$)

$A$ liquid of specific heat $0.8 \ cal / g^{\circ} C$ at temperature $60^{\circ} C$ is mixed with another liquid of the same mass having temperature $45^{\circ} C$. If the temperature of the mixture is $53^{\circ} C$,then the specific heat (in $cal / g^{\circ} C$) of the second liquid is:

$37 \ g$ of ice at $0^{\circ} C$ is mixed with $74 \ g$ of water at $70^{\circ} C$. What is the resultant temperature (in $^{\circ} C$)? (Specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$ and latent heat of fusion of ice $= 80 \ cal \ g^{-1}$)