The height of Victoria Falls is $63 \ m$. What is the difference in temperature of water at the top and at the bottom of the fall? (In $^{\circ}C$)
[Given $1 \ cal = 4.2 \ J$ and specific heat of water $= 1 \ cal \ g^{-1} \ ^{\circ}C^{-1}$]

If two balls of the same metal weighing $5\, g$ and $10\, g$ strike a target with the same velocity,and the heat energy developed is used solely for raising their temperature,then the temperature rise will be higher:

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

$A$ thermocouple develops $40\,\mu V/K$. If the hot and cold junctions are at $40\,^{\circ}C$ and $20\,^{\circ}C$ respectively,then the emf developed by a thermopile using $150$ such thermocouples in series shall be ............... $mV$.

If in the winter season the surface temperature of a lake is $1^{\circ} C$,the temperature at the bottom of the lake will be ............

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).