$A$ $10 \,kW$ 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 $900 \,J \,kg^{-1} \,K^{-1}$)

$A$ $10 \ W$ electric heater is used to heat a container filled with $0.5 \ kg$ of water. It is found that the temperature of the water and the container rises by $3 \ K$ in $15 \ min$. The container is then emptied, dried, and filled with $2 \ kg$ of oil. The same heater now raises the temperature of the container-oil system by $2 \ K$ in $20 \ min$. Assuming that there is no heat loss in the process and the specific heat of water is $4200 \ J \ kg^{-1} \ K^{-1}$, the specific heat of oil in the same unit is equal to:

$1\,\,kg$ of ice at $-10^{\circ}C$ is mixed with $4.4\,\,kg$ of water at $30^{\circ}C$. The final temperature of the mixture is $........^{\circ}C$ (specific heat of ice is $2100\,\,J/kg/K$ and latent heat of fusion of ice is $336000\,\,J/kg$)

$A$ calorimeter contains $0.5 \,kg$ of water at $30^{\circ} C$. When $0.3 \,kg$ of water at $60^{\circ} C$ is added to it, the resulting temperature is found to be $40^{\circ} C$. The water equivalent of the calorimeter is (in $\,kg$)

$2\, kg$ of ice at $-20^{\circ}C$ is mixed with $5\, kg$ of water at $20^{\circ}C$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $1\, kcal/kg/^{\circ}C$ and $0.5\, kcal/kg/^{\circ}C$ respectively,while the latent heat of fusion of ice is $80\, kcal/kg$.

One kilogram of ice at $0^{\circ}C$ is mixed with one kilogram of water at $80^{\circ}C$. The final temperature of the mixture is ........ $^{\circ}C$. (Take: specific heat of water $= 4200 \ J \ kg^{-1} \ K^{-1}$,latent heat of ice $= 336 \ kJ \ kg^{-1}$)