$50\, g$ of ice at $0\,^{\circ}C$ is dropped into a calorimeter containing $100\, g$ of water at $30\,^{\circ}C$. If the thermal capacity of the calorimeter is zero,then the amount of ice left in the mixture at equilibrium is ........ $g$.

Ice at $0^oC$ is added to $200\,g$ of water initially at $70^oC$ in a vacuum flask. When $50\,g$ of ice has been added and has all melted,the temperature of the flask and contents is $40^oC$. When a further $80\,g$ of ice has been added and has all melted,the temperature of the whole is $10^oC$. Calculate the specific latent heat of fusion of ice. [Take $S_w = 1\,cal/g^oC$.]

$1\, kg$ 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 = $3.36 \times 10^5\, J/kg$)

$20 \, g$ of boiling water is poured into an ice-cold brass vessel (specific heat $0.1 \, cal/g-^{\circ}C$) of mass $100 \, g$. The resulting temperature is ........ $^{\circ}C$.

When $0.4 \ kg$ of water at $30^{\circ} C$ is mixed with $0.15 \ kg$ of water at $25^{\circ} C$ in a calorimeter,the final temperature is found to be $27^{\circ} C$. Find the water equivalent of the calorimeter. (in $kg$)

$M$ grams of steam at $100^{\circ} C$ is mixed with $200 \; g$ of ice at its melting point in a thermally insulated container. If it produces liquid water at $40^{\circ} C$ [heat of vaporization of water is $540 \; cal/g$ and heat of fusion of ice is $80 \; cal/g$],the value of $M$ is: