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?

$M \ kg$ of water at $t^{\circ} C$ is divided into two parts so that one part of mass $m \ kg$ when converted into ice at $0^{\circ} C$ would release enough heat to vaporize the other part. Then $\frac{m}{M}$ is equal to (Specific heat of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$,Latent heat of fusion of ice $= 80 \ cal \ g^{-1}$,Latent heat of steam $= 540 \ cal \ g^{-1}$)

$A$ thermoelectric emf of $200 \, \mu V$ is generated between $0 \, ^oC$ and $100 \, ^oC$. The emf generated between $(0 \, ^oC - 32 \, ^oC)$ and $(32 \, ^oC - 70 \, ^oC)$ are $64 \, \mu V$ and $76 \, \mu V$ respectively. What is the thermo $emf$ generated between $(70 \, ^oC - 100 \, ^oC)$ in $\mu V$?

$A$ thermocouple develops $40\,\mu V/K$. If the hot and cold junctions are at $40\,^{\circ}C$ and $20\,^{\circ}C$ respectively,then the emf developed by a thermopile using $150$ such thermocouples in series shall be ............... $mV$.

$A$ copper ring has a diameter of exactly $25 \, mm$ at its temperature of $0^o C$. An aluminium sphere has a diameter of exactly $25.05 \, mm$ at its temperature of $100^o C$. The sphere is placed on top of the ring and the two are allowed to come to thermal equilibrium,with no heat being lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. The ratio of the mass of the sphere to the ring is: (Given: $\alpha_{Cu} = 17 \times 10^{-6} /^o C$,$\alpha_{Al} = 2.3 \times 10^{-5} /^o C$,specific heat of $Cu = 0.0923 \, cal/g^o C$,and specific heat of $Al = 0.215 \, cal/g^o C$)

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 $56\;atm$?