Final answer:
A tile floor feels colder than a rug when walked on with bare feet because it has a higher rate of heat transfer, quickly drawing heat away from your feet.
Step-by-step explanation:
On bare feet, a tile floor feels colder than a rug because the tile has a greater rate of heat transfer due to its thermal conductivity. When you walk barefoot across a carpet and then onto a tile floor, even though both surfaces are at the same temperature, the tile draws heat from your feet more quickly. This is because materials like tile typically have higher thermal conductivities compared to carpet, causing your body to lose heat at a faster rate when in contact with the tile. Your sensations of warmth or coldness are largely dependent on how fast heat is transferred from your body to the material you are touching.