When $54 \ g$ of ice at $-20^{\circ} C$ is mixed with $25 \ g$ of steam at $100^{\circ} C$, then the final mixture at thermal equilibrium contains

$10\, g$ of a lead bullet travelling at $300\, m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of the heat produced is absorbed by the bullet,the increase in its temperature is ........ $^\circ C$. (Specific heat of lead $= 150\, J/kg\cdot K$)

$A$ lead bullet at $27^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,find the velocity of the bullet at the time of striking in $m/s$. (Melting point of lead $= 327^{\circ}C$,specific heat of lead $= 0.03 \, cal/g^{\circ}C$,latent heat of fusion of lead $= 6 \, cal/g$,and $J = 4.2 \, J/cal$)

$A$ glass flask of volume $200 \, cm^3$ is just filled with mercury at $20^{\circ} C$. The amount of mercury that will overflow when the temperature of the system is raised to $100^{\circ} C$ is ........ $cm^3$ $(\gamma_{\text{glass}} = 1.2 \times 10^{-5} /^{\circ}C, \gamma_{\text{mercury}} = 1.8 \times 10^{-4} /^{\circ}C)$

How many $J$ of heat energy is required to convert $1\,g$ of ice at $-10^{\circ}C$ into steam at $100^{\circ}C$?

Explain why:
$(a)$ Two bodies at different temperatures $T_1$ and $T_2$,if brought in thermal contact,do not necessarily settle to the mean temperature $(T_1 + T_2) / 2$.
$(b)$ The coolant in a chemical or a nuclear plant (i.e.,the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.
$(c)$ Air pressure in a car tyre increases during driving.
$(d)$ The climate of a harbour town is more temperate than that of a town in a desert at the same latitude.