$A$ thin-walled cylindrical metal vessel with a linear coefficient of expansion $10^{-3} \ ^\circ C^{-1}$ contains benzene with a volume expansion coefficient of $10^{-3} \ ^\circ C^{-1}$. If the vessel and its contents are heated by $10 \ ^\circ C$,the pressure due to the liquid at the bottom:

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.

One $kg$ of water, at $20, ^oC$, is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20, \Omega$. The rms voltage in the mains is $200, V$. Ignoring heat loss from the kettle, the time taken for water to evaporate fully is close to.......... $min$. [Specific heat of water $= 4200, J/kg, ^oC$, Latent heat of water $= 2260, kJ/kg$]

How many $J$ of heat energy is required to convert $1\,g$ of ice at $-10^{\circ}C$ into steam at $100^{\circ}C$?

$5 \text{ g}$ of steam at $100^{\circ} \text{C}$ is mixed with $5 \text{ g}$ of ice at $0^{\circ} \text{C}$. What is the final temperature of the mixture (in $^{\circ} \text{C}$)?

When the pressure on water is increased,the boiling temperature of water as compared to $100^{\circ}C$ will be: