$22320 \ cal$ of heat is supplied to $100 \ g$ of ice at $0^{\circ} C$. If the latent heat of fusion of ice is $80 \ cal \ g^{-1}$ and latent heat of vaporization of water is $540 \ cal \ g^{-1}$,the final amount of water thus obtained and its temperature respectively are:

$10\, g$ 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 $= 150\, J/kg\cdot K$)

Fill in the blanks:
$(a)$ The $SI$ unit of the Stefan-Boltzmann constant is ...... .
$(b)$ In the thermal steady state of a rod,the temperature gradient is $5\,^{\circ}C/cm$ and the temperature of its hot end is $100\,^{\circ}C$. Then,at a distance of ........ $cm$ from the hot end,its temperature becomes $60\,^{\circ}C$.
$(c)$ At ...... temperature,the coefficient of volume expansion of water is zero.

$A$ metal block is made from a mixture of $2.4 \ kg$ of aluminium,$1.6 \ kg$ of brass,and $0.8 \ kg$ of copper. The metal block is initially at $20^{\circ} C$. If the heat supplied to the metal block is $44.4 \ cal$,find the final temperature of the block if the specific heats of aluminium,brass,and copper are $0.216, 0.0917, 0.0931 \ cal \cdot kg^{-1} \cdot ^{\circ}C^{-1}$ respectively. (in $^{\circ} C$)

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

$A$ thermocouple produces $40 \, \mu V/K$. The temperatures of the cold and hot junctions are $40 \, ^\circ C$ and $20 \, ^\circ C$ respectively. If $150$ such thermocouples are connected in series,what is the total thermo-emf produced in $mV$?