It has been suggested that a home can be air conditioned without the need for active equipment. Instead, outside air is routed through a long pipe that is buried underground (figure on left). Since the air temperature is higher than the ground temperature, the air will cool down prior to entering the house. An actual calculation of what happens is complex for several reasons, including (i) how rapidly air would enter the house driven by convection alone, and (ii) how rapidly heat energy can be transferred into the ground. Here, we make some simplifying assumptions to assess what is even possible. - Consider that the ground temperature around the buried pipe, in summer, is a constant 70F. - Refer to the Feb. 22 lecture on ZEROS, slides 3, 11, 12. We will use Denver to represent a hot and dry climate, and Miami to represent a hot and wet climate. a. The home is occupied by 2 average persons. How many liters per minute of outside air must be supplied to maintain the interior at a CO2 concentration of 1000 ppm? b. In Denver, the outside air is 95F and the humidity ratio is 0.010. Can passive cooling possibly deliver air that is within the human comfort zone (the given rectangles)? Briefly explain. c. In Miami, the outside air is 95F and the humidity ratio is 0.020. Can passive cooling possibly deliver air that is within the human comfort zone? Briefly explain. d. Moisture can be removed from air by active cooling using a heat pump: when the temperature of the air reaches 100% relative humidity, it is at the dew point; upon further cooling, moisture is removed by condensation on the surfaces (fins) of the evaporator. In Miami, to what temperature must you cool the air to drive the humidity ratio down to 0.010? (Your answer explains why passive cooling, part b., might be plausible in desert climates, but active cooling, part c., is required in moist climates.) e. Passive cooling, part b., changes the temperature but not the humidity ratio of the air. Assume that the flow of air calculated in part a. is cooled in the pipe from 95 to 80F. How much power must be transferred from the air to the ground? f. The passive cooling pipe has a length of 30 m and a diameter of 15 cm. Assume that air cooling take place uniformly along the pipe (which is not true, but we are keeping things simple). What is the average power per unit area of pipe wall? How does this number compare with the maximum heat flux available in shallow ground-source heating of ~ 5 W/m2?