$A$ flask of volume $10^3 \ cc$ is completely filled with mercury at $0 \, ^oC$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6} / ^oC$ and that of glass is $40 \times 10^{-6} / ^oC$. If the flask is now placed in boiling water at $100 \, ^oC$,how much mercury (in $cc$) will overflow?

Give one example each for solid,liquid,and gas showing expansion with an increase in temperature and contraction with a decrease in temperature.

$A$ clock pendulum having a coefficient of linear expansion $\alpha = 9 \times 10^{-7} /^{\circ}C$ has a period of $0.5 \ s$ at $20^{\circ}C$. If the clock is used in a climate where the temperature is $30^{\circ}C$,how much time does the clock lose in each oscillation? (Assume $g$ is constant)

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 $, g$)

$A$ calorimeter of mass $0.2 \ kg$ and specific heat $900 \ J/kg \cdot K$ contains $0.5 \ kg$ of a liquid of specific heat $2400 \ J/kg \cdot K$. Its temperature falls from $60^{\circ}C$ to $55^{\circ}C$ in one minute. The rate of cooling is ....... $J/s$.

Answer the following questions based on the $P$ - $T$ phase diagram of carbon dioxide:
$(a)$ At what temperature and pressure can the solid,liquid and vapour phases of $CO_{2}$ co-exist in equilibrium?
$(b)$ What is the effect of decrease of pressure on the fusion and boiling point of $CO_{2}$?
$(c)$ What are the critical temperature and pressure for $CO_{2}$? What is their significance?
$(d)$ Is $CO_{2}$ solid,liquid or gas at $(i)$ $-70^{\circ}C$ under $1\;atm$,$(ii)$ $-60^{\circ}C$ under $10\;atm$,$(iii)$ $15^{\circ}C$ under $56\;atm$?