Thermal energy is added to four identical samples of water what increases in each sample

Average speed of a molecule

Explanation:

If thermal energy (heat) is added to a substance or sample, according to the first law of thermodynamics this will cause the internal energy in that sample to increase.

The increase in internal energy will be manifested in that the speed of the  molecules that make up the substance will increase, and therefore the average speed  of a molecule increases.