$2 \ g$ 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 $cal/g$.

$A$ beaker contains $200\,g$ of water. The heat capacity of the beaker is equal to that of $20\,g$ of water. The initial temperature of water in the beaker is $20\,^{\circ}C$. If $440\,g$ of hot water at $92\,^{\circ}C$ is poured in it,the final temperature (neglecting radiation loss) will be nearest to ........ $^{\circ}C$.

The time taken for a calorimeter containing $75 \ g$ of water at $62^{\circ} C$ to cool to $58^{\circ} C$ is $9 \ minutes$. When the calorimeter contains $105 \ g$ of water,it takes $12 \ minutes$ to cool from $62^{\circ} C$ to $58^{\circ} C$. The water equivalent of the calorimeter is $.........$ (in $g$)

$A$ vessel contains $110\,g$ of water. The heat capacity of the vessel is equivalent to $10\,g$ of water. The initial temperature of the water in the vessel is $10\,^{\circ}C$. If $220\,g$ of hot water at $70\,^{\circ}C$ is poured into the vessel,the final temperature,neglecting radiation loss,will be nearly equal to ........ $^{\circ}C$.

$1 \text{ kg}$ of steam at $150^{\circ} \text{C}$ is passed from a steam chamber into a copper coil immersed in $20 \text{ L}$ of water. The steam condenses in the coil and is returned to the steam chamber as water at $90^{\circ} \text{C}$. The latent heat of steam is $540 \text{ cal g}^{-1}$,and the specific heat of steam is $1 \text{ cal g}^{-1} {}^{\circ} \text{C}^{-1}$. The rise in temperature of the water is: (in $^{\circ} \text{C}$)

Steam at $100^{\circ}C$ is passed into a calorimeter containing $1\,kg$ of water with a water equivalent of $0.02\,kg$ at $15^{\circ}C$ until the temperature of the calorimeter rises to $80^{\circ}C$. The mass of the steam condensed is $.....\,kg$. (Given: $L = 536\,cal/g$,specific heat of water $c = 1\,cal/g^{\circ}C$)