A hygrometer is used to measure the moisture content of humid air. Calibration of the instrument leads to a straight line on a semi log plot of y, the mole fraction of water in air (logarithmic scale), versus H, the instrument reading (linear scale). Room air is charged into the hygrometer sample chamber on a day when the temperature is 22°C, barometric pressure is 1.00 atm. and the relative humidity is 40%. The resulting meter reading is H = 5.0. A second measurement is then made by heating water to 50°C in a sealed flask containing air. The system is allowed to equilibrate at a pressure of 839 mm Hg with liquid still present in the flask, and a sample of the air above the liquid is withdrawn and injected into the sample chamber (which is heated to prevent condensation). The meter reading in this case is H = 48.

(a) Determine the expression for y as a (unction of H.

(b) Suppose you wish to condition air at 35°C and 1 atm to produce air at 22°C, 1 atm. and 40% relative humidity. The air conditioner first cools the air, condensing the necessary amount of water, and then reheats the remaining air to 22°C. A sample of the outside air is injected into the hygrometer chamber, and the resulting reading is H = 30. Calculate the temperature to which the air must be cooled before it is reheated and determine the amount of water condensed in kg/rn3 of delivered conditioned air.