Thermodynamics

724 | ThermodynamicsThus,Energy balance:m # f m # a 1v 2 v 1 2E # in E # out1since Q # 0 and W # 02orm # a h 1 m # f h f2 m # a h 2Dividing by ṁ a givesm # a h 1 m # a 1v 2 v 1 2h f2 m # a h 2orwhich yieldsh 1 1v 2 v 1 2h f2 h 21c p T 1 v 1 h g12 1v 2 v 1 2h f2 1c p T 2 v 2 h g22where, from Eq. 14–11b,v 1 c p 1T 2 T 1 2 v 2 h fg2h g1 h f2v 2 0.622P g 2P 2 P g2(14–14)(14–15)OrdinarythermometerWet-bulbthermometerAirflowWickLiquidwaterFIGURE 14–12A simple arrangement to measure thewet-bulb temperature.since f 2 100 percent. Thus we conclude that the specific humidity (andrelative humidity) of air can be determined from Eqs. 14–14 and 14–15 bymeasuring the pressure and temperature of air at the inlet and the exit of anadiabatic saturator.If the air entering the channel is already saturated, then the adiabatic saturationtemperature T 2 will be identical to the inlet temperature T 1 , in whichcase Eq. 14–14 yields v 1 v 2 . In general, the adiabatic saturation temperatureis between the inlet and dew-point temperatures.The adiabatic saturation process discussed above provides a means ofdetermining the absolute or relative humidity of air, but it requires a longchannel or a spray mechanism to achieve saturation conditions at the exit. Amore practical approach is to use a thermometer whose bulb is covered witha cotton wick saturated with water and to blow air over the wick, as shown inFig. 14–12. The temperature measured in this manner is called the wet-bulbtemperature T wb , and it is commonly used in air-conditioning applications.The basic principle involved is similar to that in adiabatic saturation.When unsaturated air passes over the wet wick, some of the water in thewick evaporates. As a result, the temperature of the water drops, creating atemperature difference (which is the driving force for heat transfer) betweenthe air and the water. After a while, the heat loss from the water by evaporationequals the heat gain from the air, and the water temperature stabilizes.The thermometer reading at this point is the wet-bulb temperature. The wetbulbtemperature can also be measured by placing the wet-wicked thermometerin a holder attached to a handle and rotating the holder rapidly,that is, by moving the thermometer instead of the air. A device that works