Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box contains one mole of helium at temperature $(7/3)$ $T_0$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases,$T_f$  in terms of $T_0$ is

A vessel contains $110\,\,g$  of water. The heat capacity of the vessel is equal to $10\,\,g$ of water. The initial temperature of water in vessel is $10\,^oC.$  If $220\,\,g$  of hot water at $70\,^oC$  is poured in the vessel, the final temperature neglecting radiation loss, will be nearly equal to …….. $^oC$

$10\,gm$ of ice at $0\,^oC$ is mixed with $'m'\,gm$ of water at $50\,^oC$ . …….. $gm$ is minimum value of $m$ so that ice melts completely. ( $L_f = 80\,cal/gm$ and $S_W = 1\,cal/gm-\,^oC$ )

If $1\; g$ of steam is mixed with $1\; g$ of ice, then the resultant temperature of the mixture is …….. $^oC$

A block of mass $2.5\,\, kg$ is heated to temperature of $500^o C$ and placed on a large ice block. ……… $kg$ is the maximum amount of ice that can melt (approx.). Specific heat for the body $= 0.1 Cal/gm^o C$.