FREE RESPONSE (4 points each; show your work): 1. Why does the bathroom tile floor feel much colder than the bathroom rug? Let's crunch some numbers to find out. Imagine one morning the wool carpet and the ceramic floor are both cold (50 .F or 10 .C). Let's assume they each have about the same thickness d of 2cm (0.02 m). Each of your feet has a surface area A of about 150 cm or 0.015 m2. When you put one foot on the tile and one foot on the rug, the bottom of your foot and top of tile/rug come to equilibrium at about 86 .F or 30 .C. Thermal K Conductivity (J/s.m."C) Wool (carpet) 0.04 TH = 30 .C TH = 30 .C Ceramic tile 0.84 = 10 C Tc = 10 C (a) Find the rate of heat transfer by conduction, in J/s, from your foot to the WOOL RUG (b) Find the rate of heat transfer by conduction, in J/s, from your foot to the TILE (c) Which are you losing heat to more quickly, the tile or the rug? Why? (d) How do your answers above help explain why the tile feels colder than the rug, even though they are at the same temperature