Three bodies of the same material and having masses $m, m$ and $3m$ are at temperatures $40^{\circ} C, 50^{\circ} C$ and $60^{\circ} C$ respectively. If the bodies are brought in thermal contact, the final temperature will be (in $^{\circ} C$)

Two different rigid boxes are placed on a table,each containing a different gas. Box $A$ contains $1 \text{ mole}$ of nitrogen gas at temperature $T_0$,and box $B$ contains $1 \text{ mole}$ of helium gas at temperature $(7/3) T_0$. If these two boxes are brought into thermal contact,heat exchange occurs until a final equilibrium temperature $T_f$ is reached. The final temperature $T_f$ is:

In a calorimeter of water equivalent $20 \,g$,water of mass $1.1 \,kg$ is taken at $288 \,K$ temperature. If steam at temperature $373 \,K$ is passed through it and the temperature of the water increases by $6.5^{\circ} C$,then the mass of steam condensed is ............ $g$.

$A$ metal block of mass $3.3 \ kg$ is heated to a temperature of $400^{\circ} C$ and then placed on a large ice block. The specific heat of the metal is $0.4 \ J \ g^{-1} \ K^{-1}$ and the latent heat of fusion of water is $330 \ J \ g^{-1}$. The maximum amount of ice that can melt is: (in $kg$)

When $0.15 \; kg$ of ice at $0^{\circ} C$ is mixed with $0.30 \; kg$ of water at $50^{\circ} C$ in a container,the resulting temperature is $6.7^{\circ} C$. Calculate the latent heat of fusion of ice. (Given: $s_{\text{water}} = 4186 \; J \; kg^{-1} \; K^{-1}$)

$200 \,g$ of ice at $-20^{\circ} C$ is mixed with $500 \,g$ of water at $20^{\circ} C$ in an insulating vessel. The final mass of water in the vessel is ........... $g$ (specific heat of ice $= 0.5 \,cal \,g^{-1} {^{\circ}C}^{-1}$,latent heat of fusion of ice $= 80 \,cal \,g^{-1}$).