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

$A$ vessel contains $110 \, g$ of water. The heat capacity of the vessel is equivalent to $10 \, g$ of water. The initial temperature of water in the vessel is $10^{\circ}C$. If $220 \, g$ of hot water at $70^{\circ}C$ is poured into the vessel,the final temperature,neglecting radiation loss,will be........ $^{\circ}C$

Two tanks $A$ and $B$ contain water at $30,^{\circ}C$ and $80,^{\circ}C$ respectively. Calculate the amount of water that must be taken from each tank to prepare $40,kg$ of water at $50,^{\circ}C$.

$0.1 \,m^{3}$ of water at $80^{\circ} C$ is mixed with $0.3 \,m^{3}$ of water at $60^{\circ} C$. The final temperature of the mixture is (in $^{\circ} C$)

$10 \, g$ of ice at $0^{\circ}C$ is mixed with $100 \, g$ of water at $50^{\circ}C$. What is the resultant temperature of the mixture in $^{\circ}C$?

$A$ glass beaker contains $200 \,g$ of carbonated water initially at $20^{\circ} C$. How much ice should be added to obtain the final temperature of $0^{\circ} C$ with all ice melted, if the initial temperature of ice is $-10^{\circ} C$ (in $\,g$)? Neglect the heat capacity of the glass.
[Take, $C_{\text{water}} = 4190 \,J/kg^{\circ} C$, $C_{\text{ice}} = 2100 \,J/kg^{\circ} C$, $L_F = 3.34 \times 10^5 \,J/kg$]