If the temperature profile through the ground is linear, increasing from 35°F at the surface by 0.5°F per foot of depth, how long will it take for a pipe buried 10 ft below the surface to reach 32°F if the outside air temperature is suddenly dropped to 0°F. The thermal diffusivity of soil may be taken as 0.02 ft²/h, its thermal conductivity is 0.8 Btu/h ft °F, and the convective heat transfer coefficient between the soil and the surrounding air is 1.5 Btu/h ft² °F.