Thermodynamics

Chapter 14 | 723starts condensing. This happens when the air reaches its dew-point temperatureT dp , which is determined from Eq. 14–13 to beT dp T sat @ PvwhereThus,P v fP g @ 20°C 10.75212.3392 kPa2 1.754 kPaT dp T sat @ 1.754 kPa 15.4 °CDiscussion Note that the inner surface of the window should be maintainedabove 15.4°C if condensation on the window surfaces is to be avoided.14–4 ADIABATIC SATURATION ANDWET-BULB TEMPERATURESRelative humidity and specific humidity are frequently used in engineeringand atmospheric sciences, and it is desirable to relate them to easily measurablequantities such as temperature and pressure. One way of determiningthe relative humidity is to determine the dew-point temperature of air,as discussed in the last section. Knowing the dew-point temperature, wecan determine the vapor pressure P v and thus the relative humidity. Thisapproach is simple, but not quite practical.Another way of determining the absolute or relative humidity is related toan adiabatic saturation process, shown schematically and on a T-s diagramin Fig. 14–11. The system consists of a long insulated channel that containsa pool of water. A steady stream of unsaturated air that has a specifichumidity of v 1 (unknown) and a temperature of T 1 is passed through thischannel. As the air flows over the water, some water evaporates and mixeswith the airstream. The moisture content of air increases during this process,and its temperature decreases, since part of the latent heat of vaporization ofthe water that evaporates comes from the air. If the channel is long enough,the airstream exits as saturated air (f 100 percent) at temperature T 2 ,which is called the adiabatic saturation temperature.If makeup water is supplied to the channel at the rate of evaporation attemperature T 2 , the adiabatic saturation process described above can be analyzedas a steady-flow process. The process involves no heat or work interactions,and the kinetic and potential energy changes can be neglected. Thenthe conservation of mass and conservation of energy relations for this twoinlet,one-exit steady-flow system reduces to the following:Mass balance:orm # a 1 m # a 2 m # am # w 1 m # f m # w 2(The mass flow rate of dry airremains constant)(The mass flow rate of vapor in theair increases by an amount equalto the rate of evaporation ṁ f )Unsaturated airT 1 , ω 1f 1T1 2Liquid waterAdiabaticsaturationtemperature2P v11Saturated airT 2 , ω 2f 2 100%Liquid waterat T 2Dew-pointtemperatureFIGURE 14–11The adiabatic saturation process andits representation on a T-s diagram ofwater.sm # av 1 m # f m # av 2