Which of the following graphs shows the variation of thermoelectric power with temperature difference $\theta$ between the hot and cold junctions in thermocouples?

$A$ 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 $J = 4.2 \, J/cal$)

$A$ steel ball of mass $0.1 \, kg$ falls freely from a height of $10 \, m$ and bounces to a height of $5.4 \, m$ from the ground. If the dissipated energy in this process is absorbed by the ball,the rise in its temperature is ........... $^\circ C$ (Specific heat of steel $= 460 \, J \, kg^{-1} \, ^\circ C^{-1}, \; g = 10 \, m \, s^{-2}$)

$1 \ gm$ of ice at $0^o C$ is mixed with $1 \ gm$ of steam at $100^o C$. What will be the final temperature $(^o C)$?

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.

$A$ 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 $\alpha$.