Of two masses of $5 \, kg$ each falling from a height of $10 \, m$,by which $2 \, kg$ of water is stirred. The rise in temperature of the water will be ........ $^\circ C$.

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of $100^{\circ} C$,while the other one is kept at $0^{\circ} C$. If the two are brought into contact,then assuming no heat loss to the environment,the final temperature that they will reach 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 $g$)

$A$ piece of metal weighing $100 \,g$ is heated to $80^{\circ} C$ and dropped into $1 \,kg$ of cold water in an insulated container at $15^{\circ} C$. If the final temperature of the water in the container is $15.69^{\circ} C$,the specific heat of the metal in $J / g^{\circ} C$ is:

$2 \; g$ of steam condenses when passed through $40 \; g$ of water initially at $25 \; ^\circ C$. The condensation of steam raises the temperature of water to $54.3 \; ^\circ C$. What is the latent heat of steam in $cal/g$?

$20 \, g$ 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 ........ $^{\circ}C$.