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.

(N/A) The Stefan-Boltzmann law is given by $E = \sigma T^4$. Thus,the unit of $\sigma$ is $W \cdot m^{-2} \cdot K^{-4}$.
$(b)$ The temperature gradient is defined as $\frac{dT}{dx} = 5\,^{\circ}C/cm$. The temperature difference $\Delta T = 100\,^{\circ}C - 60\,^{\circ}C = 40\,^{\circ}C$. The distance $x$ is given by $x = \frac{\Delta T}{dT/dx} = \frac{40}{5} = 8\,cm$.
$(c)$ The coefficient of volume expansion of water is zero at $4\,^{\circ}C$ because water has maximum density at this temperature.