A heater is used to boil water in a container. The heater supplies heat at a constant rate R. Water boils at 100 °C. Assume that the water in the container loses heat to the atmosphere at a rate that is proportional to both, the temperature of the water as well as to the volume of water in the container. If this proportionality constant is K then the maximum volume of water that can be boiled by the heater is

Correct option is C

Solution:

Heater supplies heat at a constant rate = R.
Heat loss happens at a rate = K × Volume × Temperature.
Temperature is given as 100°C, so Heat loss rate = 100 × K × V.
For maximum boiling, Heat supplied = Heat lost.
Thus,
R = 100 × K × V
Now solving for V,
V = R / (100 × K)
Thus, maximum volume V = R/100K.
Hence, the correct answer is (c).

Trick to Remember:
When the question says loss is proportional to volume and temperature, just equate heat supply = heat loss, and solve for volume.

Information Booster:
Such problems are based on the idea of "steady state" where supply and loss balance out.
The proportionality constant K depends on container and surroundings.