The height of a waterfall is $50 \ m$. If $g = 9.8 \ m/s^2$, the difference between the temperature at the top and the bottom of the waterfall is: (in $^{\circ} C$)

Two identical balls,$A$ and $B$,of uniform composition and initially at the same temperature,each absorb exactly the same amount of heat. $A$ is hanging from the ceiling while $B$ rests on the horizontal floor in the same room. Assuming no subsequent heat loss by the balls,which of the following statements is correct about their final temperatures,$T_A$ and $T_B$,once the balls have reached their final state?

One quality of a thermometer is that its heat capacity should be small. If $P$ is a mercury thermometer,$Q$ is a resistance thermometer,and $R$ is a thermocouple type,then:

$A$ 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 ....... $J/s$.

$A$ steel ball of mass $0.1 \, kg$ falls freely from a height of $10 \, m$ and bounces to a height of $5.4 \, m$ from the ground. If the dissipated energy in this process is absorbed by the ball,the rise in its temperature is ........... $^\circ C$ (Specific heat of steel $= 460 \, J \, kg^{-1} \, ^\circ C^{-1}, \; g = 10 \, m \, s^{-2}$)

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 $56\;atm$?