The water equivalent of $20 \,g$ of aluminium (specific heat $0.2 \,cal \,g^{-1} {}^{\circ}C^{-1}$) is ......... $g$.

$A$ calorimeter has a heat capacity of $100 \ J/K$ and is at $30^{\circ}C$. $100 \ g$ of water at $40^{\circ}C$ (specific heat capacity $4200 \ J/kg \cdot K$) is poured into the calorimeter. What is the final temperature of the mixture in the calorimeter in $^{\circ}C$?

Two liquids $A$ and $B$ are at temperatures of $75^{\circ} C$ and $15^{\circ} C$. Their masses are in the ratio of $2: 3$ and their specific heats in the ratio $3: 4$. If these two liquids are mixed,then the resulting temperature will be $...^{\circ} C$.

When $50 \ g$ of water at $10^{\circ} C$ is mixed with $50 \ g$ of water at $100^{\circ} C$,the resultant temperature is: (in $^{\circ} C$)

$m$ g of water at $30^{\circ} C$ is mixed with $5$ g of ice at $-20^{\circ} C$. If the final equilibrium temperature of the mixture is $6^{\circ} C$,find the value of $m$. (Given: specific heat capacity of ice $= 0.5 \text{ cal g}^{-1} {}^{\circ} C^{-1}$,specific heat capacity of water $= 1 \text{ cal g}^{-1} {}^{\circ} C^{-1}$,and latent heat of fusion of ice $= 80 \text{ cal g}^{-1}$) (in $g$)

$2\, kg$ of ice at $-20^{\circ}C$ is mixed with $5\, kg$ of water at $20^{\circ}C$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $1\, kcal/kg/^{\circ}C$ and $0.5\, kcal/kg/^{\circ}C$ respectively,while the latent heat of fusion of ice is $80\, kcal/kg$.