$A$ lead ball moving with a velocity $V$ strikes a wall and stops. If $50\%$ of its energy is converted into heat,then what will be the increase in temperature? (Specific heat of lead is $S$)

The heat extracted out of $x \ \text{g}$ of water initially at $50^\circ \text{C}$ to cool it down to $0^\circ \text{C}$ is sufficient to evaporate $(1000 - x) \ \text{g}$ of water also initially at $50^\circ \text{C}$. The value of $x$ (closest integer) is . . . . . . . (Take latent heat of water $L = 2256 \ \text{kJ/kg}$, specific heat capacity of water $c = 4200 \ \text{J/kg}\cdot \text{K}$)

On which of the following four processes does the functioning of a bimetallic strip depend?
$(i)$ Radiation
$(ii)$ Energy conversion
$(iii)$ Melting
$(iv)$ Thermal expansion

An iron rod of heat capacity $C$ is heated to temperature $8T_0$. It is then put in a cylindrical vessel of adiabatic walls having two moles of air which can be treated as a diatomic ideal gas at temperature $T_0$ and closed by a movable piston which is also adiabatic. The atmospheric pressure is $P_0$. The cylinder with the piston combined have a heat capacity $2C$. Find the equilibrium temperature. (Assume the temperature of air to be uniform and equal to the vessel at all times).

$A$ stationary object at $4^{\circ} C$ and weighing $3.5 \ kg$ falls from a height of $2000 \ m$ on a snow mountain at $0^{\circ} C$. If the temperature of the object just before hitting the snow is $0^{\circ} C$ and the object comes to rest immediately,then the quantity of ice that melts is (Acceleration due to gravity $= 10 \ m/s^2$,Latent heat of ice $= 3.5 \times 10^5 \ J/kg$)

$A$ steel pendulum clock manufactured at $32^{\circ} C$ and working at $47^{\circ} C$ is nearly (Coefficient of linear expansion of steel $= 12 \times 10^{-6} /{ }^{\circ} C$)