How many grams of ice at $0 \, ^\circ \text{C}$ will be melted by $1 \, \text{g}$ of steam at $100 \, ^\circ \text{C}$? (Latent heat of fusion of ice $L = 80 \, \text{cal/g}$ and latent heat of vaporization of water $L' = 540 \, \text{cal/g}$)

Pure water supercooled to $-15^{\circ} C$ is contained in a thermally insulated flask. $A$ small amount of ice is thrown into the flask. The fraction of water frozen into ice is:

Three liquids with masses $m_1, m_2, m_3$ are thoroughly mixed. If their specific heats are $c_1, c_2, c_3$ and their temperatures are $T_1, T_2, T_3$ respectively,then the temperature of the mixture is

Steam at $100^{\circ} C$ is passed into $1 \, kg$ of water contained in a calorimeter at $9^{\circ} C$ until the temperature of the water and calorimeter increases to $90^{\circ} C$. The mass of the steam condensed is nearly (water equivalent of calorimeter $= 0.1 \, kg$, specific heat of water $= 1 \, cal \cdot g^{-1} \cdot {}^{\circ} C^{-1}$, and latent heat of vaporisation $= 540 \, cal \cdot g^{-1}$). (in $g$)

$A$ liquid of mass $2m$ and specific heat $C$ is heated to a temperature $4T$. Another liquid of mass $m$ and specific heat $2C$ is heated to a temperature $T$. If these two liquids are mixed,the resulting temperature of the mixture is:

The $SI$ unit of mechanical equivalent of heat is