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:

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

$4 \text{ g}$ of steam at $100^{\circ} C$ is added to $20 \text{ g}$ of water at $46^{\circ} C$ in a container of negligible mass. Assuming no heat is lost to the surroundings, the mass of water in the container at thermal equilibrium is. (Latent heat of vaporisation $= 540 \text{ cal/g}$, Specific heat of water $= 1 \text{ cal/g}^{\circ} C$):- (in $\text{ g}$)

$A$ $10 \,kW$ drilling machine is used to drill a bore in an aluminium block of mass $25 \,kg$. If the machine is on for $3 \,minutes$ and $50 \%$ of the heat liberated is absorbed by the block, what is the rise in temperature of the block (in $^{\circ} C$)? (Specific heat of aluminium is $900 \,J \,kg^{-1} \,K^{-1}$)

$A$ kettle with $2\, L$ of water at $27\, ^oC$ is heated by a coil heater with a power of $1\, kW$. The heat is lost to the atmosphere at a constant rate of $160\, J/s$ when its lid is open. In how much time will the water be heated to $77\, ^oC$ (specific heat of water $= 4.2\, kJ/(kg \cdot K)$) with the lid open?

Two liquids $A$ and $B$ are at $32^{\circ}C$ and $24^{\circ}C$. When mixed in equal masses,the temperature of the mixture is found to be $28^{\circ}C$. Their specific heats are in the ratio of: