$10\,g$ of ice at $-20\,^{\circ}C$ is dropped into a calorimeter containing $10\,g$ of water at $10\,^{\circ}C$. The specific heat of water is twice that of ice. When equilibrium is reached,the calorimeter will contain

$80\, g$ 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 ........ $g$.

$1 \ g$ of ice at $0^\circ C$ is mixed with $1 \ g$ of water at $100^\circ C$. The resulting temperature will be .......... $^\circ C$.

How many grams of a liquid with a specific heat of $0.2 \, cal/g^{\circ}C$ at a temperature of $40^{\circ}C$ must be mixed with $100 \, g$ of a liquid with a specific heat of $0.5 \, cal/g^{\circ}C$ at a temperature of $20^{\circ}C$,so that the final temperature of the mixture becomes $32^{\circ}C$?

Steam at $100^{\circ} C$ is passed into $1 \ kg$ of water contained in a calorimeter of water equivalent $0.2 \ kg$ at $9^{\circ} C$ until the temperature of the calorimeter and water in it increases to $90^{\circ} C$. The mass of steam condensed in $kg$ is nearly (specific heat of water $= 1 \ cal/g^{\circ} C$, latent heat of vaporisation $= 540 \ cal/g$)

$10 \, g$ 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 $^{\circ}C$?