How many grams of a liquid with a specific heat of $0.2 \, cal/g^{\circ}C$ at a temperature of $40^{\circ}C$ must be mixed with $100 \, g$ of a liquid with a specific heat of $0.5 \, cal/g^{\circ}C$ at a temperature of $20^{\circ}C$,so that the final temperature of the mixture becomes $32^{\circ}C$?

$A$ $2100 W$ 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 ....... $^{\circ}C$.

$A$ water heater of power $2000\,W$ is used to heat water. The specific heat capacity of water is $4200\,J\,kg^{-1}\,K^{-1}$. The efficiency of the heater is $70\%$. The time required to heat $2\,kg$ of water from $10^{\circ}C$ to $60^{\circ}C$ is $..........s$. (Assume that the specific heat capacity of water remains constant over the temperature range).

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

Water is kept in a thermally insulated container at a temperature of $-10^{\circ}C$. If a small piece of ice is dropped into it, what will be the ratio of the mass of ice formed from the water to the initial mass of water?

$A$ liquid of specific heat $0.8 \ cal / g^{\circ} C$ at temperature $60^{\circ} C$ is mixed with another liquid of the same mass having temperature $45^{\circ} C$. If the temperature of the mixture is $53^{\circ} C$,then the specific heat (in $cal / g^{\circ} C$) of the second liquid is: