Steam is passed into $22 \, g$ of water at $20^{\circ}C$. The mass of water that will be present when the water acquires a temperature of $90^{\circ}C$ is ........ $g$. (Latent heat of steam is $540 \, cal/g$)

$A$ calorimeter contains $0.5 \,kg$ of water at $30^{\circ} C$. When $0.3 \,kg$ of water at $60^{\circ} C$ is added to it, the resulting temperature is found to be $40^{\circ} C$. The water equivalent of the calorimeter is (in $\,kg$)

$80\, g$ of water at $30^{\circ}C$ is poured on a large block of ice at $0^{\circ}C$. The mass of ice that melts is ........ $g$.

$1\, kg$ of ice at $-10\,^{\circ}C$ is mixed with $4.4\, kg$ of water at $30\,^{\circ}C$. The final temperature of the mixture is ........ $^{\circ}C$. (Specific heat of ice = $2100\, J/kg\cdot K$,specific heat of water = $4200\, J/kg\cdot K$,latent heat of fusion of ice = $3.36 \times 10^5\, J/kg$)

When $M_1$ gram of ice at $-10\,^{\circ}C$ (specific heat $= 0.5\, cal\, g^{-1}\,^{\circ}C^{-1}$) is added to $M_2$ gram of water at $50\,^{\circ}C$,finally no ice is left and the water is at $0\,^{\circ}C$. The value of latent heat of ice,in $cal\, g^{-1}$ is

$m$ 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 $g$)