$A$ waterfall is $84 \ m$ high. If half of the potential energy of the falling water gets converted to heat,the rise in temperature of the water will be: (in $^\circ C$)

$A$ lead bullet at $27\ ^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle,the velocity of the bullet at the time of striking is ....... $m/s$. (Melting point of lead $= 327\ ^oC$,specific heat of lead $= 0.03\ cal/g\ ^oC$,latent heat of fusion of lead $= 6\ cal/g$,and $J = 4.2\ J/cal$)

What are freezing and freezing point?

$ 1 \text{ g} $ of ice is mixed with $ 1 \text{ g} $ of steam. At thermal equilibrium,the temperature of the mixture is (in $^{\circ} C$)

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 $56\;atm$?

$A$ stationary object at $4^{\circ} C$ and weighing $3.5 \ kg$ falls from a height of $2000 \ m$ on a snow mountain at $0^{\circ} C$. If the temperature of the object just before hitting the snow is $0^{\circ} C$ and the object comes to rest immediately,then the quantity of ice that melts is (Acceleration due to gravity $= 10 \ m/s^2$,Latent heat of ice $= 3.5 \times 10^5 \ J/kg$)