$20 \, g$ 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 $100 \ g$ of boiling water at $100^{\circ} C$ is added into a calorimeter containing $300 \ g$ of cold water at $10^{\circ} C$, the temperature of the mixture becomes $20^{\circ} C$. Then, a metallic block of mass $1 \ kg$ at $10^{\circ} C$ is dipped into the mixture in the calorimeter. After reaching thermal equilibrium, the final temperature becomes $19^{\circ} C$. What is the specific heat of the metal in $C$.$G$.$S$. units?

$200 \, g$ of a solid ball at $20 \, ^\circ C$ is dropped in an equal amount of water at $80 \, ^\circ C$. The resulting temperature is $60 \, ^\circ C$. This means that the specific heat of the solid is

$A$ calorimeter of water equivalent $20 \, g$ contains $180 \, g$ of water at $25^{\circ} C$. '$m$' grams of steam at $100^{\circ} C$ is mixed in it until the temperature of the mixture is $31^{\circ} C$. The value of '$m$' is close to (Latent heat of water $= 540 \, \text{cal} \, g^{-1}$,specific heat of water $= 1 \, \text{cal} \, g^{-1} {}^{\circ} C^{-1}$)

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 $kg$)

$A$ $2100 W$ continuous flow geyser (instant geyser) has water inlet temperature $= 10^{\circ}C$ while the water flows out at the rate of $20\,g/s$. The outlet temperature of water must be about ....... $^{\circ}C$.