The soil temperature in the upper layers of the earth varies with the variations in the atmospheric conditions. Before a cold front moves in, the earth at a location is initially at a uniform temperature of 10°C. Then, the area is subjected to a temperature of â8°C and high winds that result in a convection heat transfer coefficient of 40 W/m2âK on the earthâs surface for a period of 10 h. Taking the properties of the soil at that location to be k = 0.9 W/mâK and α = 1.6Ã10â5 m2/s, determine the soil temperature at distances 0, 10, 20, and 50 cm from the earthâs surface at the end of this 10-h period.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.