Final answer:
The bathroom tile feels colder due to its higher thermal conductivity, which leads to a faster heat transfer from your skin compared to a rug.
Step-by-step explanation:
The tile on a bathroom floor feels colder than a rug even though both are at the same temperature because of the higher thermal conductivity of the tile. Thermal conductivity is a material's ability to conduct heat; hence materials with higher thermal conductivity, such as tile, remove heat from your skin more quickly than those with lower thermal conductivity, such as a rug. This increased rate of heat transfer gives the sensation that the tile is colder, even though its actual temperature is the same as that of the rug.