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

$2 \; g$ of steam condenses when passed through $40 \; g$ of water initially at $25 \; ^\circ C$. The condensation of steam raises the temperature of water to $54.3 \; ^\circ C$. What is the latent heat of steam in $cal/g$?

Two different rigid boxes are placed on a table,each containing a different gas. Box $A$ contains $1 \text{ mole}$ of nitrogen gas at temperature $T_0$,and box $B$ contains $1 \text{ mole}$ of helium gas at temperature $(7/3) T_0$. If these two boxes are brought into thermal contact,heat exchange occurs until a final equilibrium temperature $T_f$ is reached. The final temperature $T_f$ is:

The temperature of $100 \,g$ of water is to be raised from $24^{\circ} C$ to $90^{\circ} C$ by adding steam at $100^{\circ} C$ to it. The mass of the steam required in this process is (latent heat of steam is $540 \,cal \,g^{-1}$). (in $\,g$)

$1\, kg$ 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 = $2100\, J/kg\cdot K$,specific heat of water = $4200\, J/kg\cdot K$,latent heat of fusion of ice = $3.36 \times 10^5\, J/kg$)

At a power station,heat is removed from the heat exchanger by cooling water at $6.7 \times 10^9 \ J$ per minute. The cooling water enters at $6.0 \ ^oC$ and leaves at $14.0 \ ^oC$. [Take the specific heat capacity of water $4200 \ J/kg \ ^oC$]. Which of the following is the rate of water flow?