$A$ drilling machine of $10 \, kW$ power is used to drill a bore in a small aluminium block of mass $8 \, kg$. If $50 \%$ of power is used up in heating the machine itself or lost to the surroundings,then the rise in temperature of the block in $2.5 \, minutes$ is ........ $^\circ C$. [Specific heat of aluminium $= 0.91 \, J/g \cdot ^\circ C$]

$A$ liquid at $30^{\circ} C$ is poured very slowly into a calorimeter at $110^{\circ} C$. The boiling point of the liquid is $80^{\circ} C$. It is observed that the first $5 \ gm$ of the liquid evaporates completely. After adding another $80 \ gm$ of the liquid,the equilibrium temperature is found to be $50^{\circ} C$. What is the ratio of the latent heat of the liquid to its specific heat? [Neglect heat exchange with the surroundings]

$A$ piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $h$ is (Latent heat of ice is $L = 3.4 \times 10^{5} \text{ J/kg}$ and $g = 10 \text{ N/kg}$) (in $\text{ km}$)

$A$ cube is subjected to a pressure $P$ on all its faces at a temperature of $0 \, ^\circ C$. By what temperature should the cube be heated so that it regains its original volume? Let the bulk modulus of the cube be $\beta$ and the coefficient of volume expansion be $\alpha$.

The amount of heat needed to heat $200 \ g$ of ice at $-10^{\circ}C$ to convert it into water at $30^{\circ}C$ is:
Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$
Specific heat capacity of water $= 4186 \ J \ kg^{-1} \ K^{-1}$
Latent heat of fusion of ice $= 3.35 \times 10^5 \ J \ kg^{-1}$ (in $J$)

$A$ block of steel of mass $2 \,kg$ slides down a rough inclined plane of inclination $\sin ^{-1}\left(\frac{3}{5}\right)$ at a constant speed. Assuming that the mechanical energy lost due to friction is used to increase the temperature of the block, calculate the rise in temperature of the block as it slides through $80 \,cm$. (Specific heat capacity of steel $= 420 \,J kg^{-1} K^{-1}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $^{\circ} C$)