On which of the following four processes does the functioning of a bimetallic strip depend?
$(i)$ Radiation
$(ii)$ Energy conversion
$(iii)$ Melting
$(iv)$ Thermal expansion

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.

For a copper-iron $(Cu-Fe)$ couple,the thermo $e.m.f.$ (temperature of cold junction $= 0\,^{\circ}C$) is given by $E = (14\theta - 0.02\theta^2)\,\mu V$. The neutral temperature will be

The thermo $e.m.f.$ produced in a thermocouple is given by the equation $E = 40\theta - \frac{\theta^2}{20}$,where $\theta$ is the temperature difference between the two junctions. The neutral temperature is ............. $^oC$.

$A$ block of steel of mass $2 \,kg$ slides down a rough inclined plane of inclination $\sin ^{-1}\left(\frac{3}{5}\right)$ at a constant speed. Assuming that the mechanical energy lost due to friction is used to increase the temperature of the block, calculate the rise in temperature of the block as it slides through $80 \,cm$. (Specific heat capacity of steel $= 420 \,J kg^{-1} K^{-1}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $^{\circ} C$)

$A$ glass flask of volume $1$ litre is fully filled with mercury at $0\,^{\circ}C$. Both the flask and mercury are now heated to $100\,^{\circ}C$. If the coefficient of volume expansion of mercury is $1.82 \times 10^{-4}/^{\circ}C$ and the coefficient of linear expansion of glass is $10 \times 10^{-6}/^{\circ}C$,the amount of mercury which is spilled out is ............ $ml$. (in $.2$)