$A$ 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 $mV$?

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.

Which of the following graphs shows the variation of thermoelectric power of a thermocouple with the temperature difference between the hot and cold junctions?

Steam is passed into $22\, g$ of water at $20^{\circ}C$. The mass of water that will be present when the water acquires a temperature of $90^{\circ}C$ is ............ $g$ (Latent heat of steam is $540\, cal/g$) (in $, g$)

The densities of wood and benzene at $0^{\circ} C$ are $880 \ kg \ m^{-3}$ and $900 \ kg \ m^{-3}$,respectively. The coefficients of volume expansion are $1.2 \times 10^{-3} \ ^{\circ}C^{-1}$ for wood and $1.5 \times 10^{-3} \ ^{\circ}C^{-1}$ for benzene. The temperature at which a piece of wood just sinks in benzene is (in $^{\circ} C$)

The heat required to convert $8 \ g$ of ice at a temperature of $-20^{\circ}C$ to steam at $100^{\circ}C$ is (Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$, specific heat capacity of water $= 4200 \ J \ kg^{-1} \ K^{-1}$, latent heat of fusion of ice $= 336 \times 10^3 \ J \ kg^{-1}$ and latent heat of steam $= 2.268 \times 10^6 \ J \ kg^{-1}$) (in $kJ$)