Steam at $100\,^{\circ}C$ is passed into $20\,g$ of water at $10\,^{\circ}C$. When water acquires a temperature of $80\,^{\circ}C$,the mass of water present will be ........ $g$. [Take specific heat of water $= 1\,cal\,g^{-1}\,^{\circ}C^{-1}$ and latent heat of steam $= 540\,cal\,g^{-1}$]

$5 \ g$ of ice at $-30^{\circ} C$ and $20 \ g$ of water at $35^{\circ} C$ are mixed together in a calorimeter. The final temperature of the mixture is (Neglect heat capacity of the calorimeter,specific heat capacity of ice $= 0.5 \ cal \ g^{-1} {}^{\circ} C^{-1}$,latent heat of fusion of ice $= 80 \ cal \ g^{-1}$,and specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$). (in $^{\circ} C$)

If an electric heater is rated at $1000\, W$, then the time required to heat one litre of water from $20\, ^oC$ to $60\, ^oC$ is

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

$2 \ g$ of steam at $100 \ ^\circ C$ is passed into $40 \ g$ of water at $25 \ ^\circ C$. The final temperature of the mixture becomes $54.3 \ ^\circ C$. Find the latent heat of vaporization of steam in $cal/g$.

The $SI$ unit of mechanical equivalent of heat is