The water main in the cities must be placed at sufficient depth below the earth’s surface to avoid freezing during extended periods of subfreezing temperatures. Determine the minimum depth at which the water main must be placed at a location where the soil is initially at 15°C and the earth’s surface temperature under the worst conditions is expected to remain at 210°C for a period of 75 days. Take the properties of soil at that location to be k = 0.7 W/m·K and α = 1.4 × 10^-5 m²/s.