In the perception of a certain man, a bucket of lukewarm water contains more thermal energy than a large tank of cold water. Correct this understanding based on the definitions of thermal energy and temperature.

Question

Accepted Answer

This understanding is incorrect if the tank of cold water is large enough. Thermal energy is the SUM of the kinetic energy of all the molecules in a substance, and it depends on both the mass of the substance and the average kinetic energy (temperature) of its molecules. While the lukewarm water in the bucket may have molecules with higher average kinetic energy (higher temperature) than the cold water, if the tank of cold water has a very large mass — that is, a much greater number of molecules — the total (summed) kinetic energy of all its molecules can be greater than that of the smaller amount of lukewarm water. Therefore, the large tank of cold water can actually contain more thermal energy than the small bucket of lukewarm water, even though its temperature is lower.