Thermodynamics

Chapter 14 | 739Properties The enthalpy of saturated liquid water is 92.28 kJ/kg at 22°Cand 146.64 kJ/kg at 35°C (Table A–4). From the psychrometric chart,h 1 42.2 kJ/kg dry airv 1 0.0087 kg H 2 O/kg dry airv 1 0.842 m 3 /kg dry airh 2 100.0 kJ/kg dry airv 2 0.0273 kg H 2 O/kg dry airAnalysis We take the entire cooling tower to be the system, which is shownschematically in Fig. 14–34. We note that the mass flow rate of liquid waterdecreases by an amount equal to the amount of water that vaporizes in thetower during the cooling process. The water lost through evaporation must bemade up later in the cycle to maintain steady operation.(a) Applying the mass and energy balances on the cooling tower givesDry air mass balance:Water mass balance:orEnergy balance:orm # a 1 m # a 2 m # am # 3 m # a 1v 1 m # 4 m # a 2v 2m # 3 m # 4 m # a 1v 2 v 1 2 m # makeupainm # h aoutm # h S m # a 1h 1 m # 3h 3 m # a 2h 2 m # 4h 4m # 3h 3 m # a 1h 2 h 1 2 1m # 3 m # makeup2h 4WARMWATER35°C100 kg/sSystemboundary100 kg/sCOOLWATER34Makeupwater22°C230°Cf 2 = 100%FIGURE 14–34Schematic for Example 14–9.1AIR1 atm20°Cf 1 = 60%V·1Solving for m· a givesm # a Substituting,m # 3 1h 3 h 4 21h 2 h 1 2 1v 2 v 1 2h 4m # 1100 kg>s231146.64 92.282 kJ>kg4a 96.9 kg>s31100.0 42.22 kJ>kg4 310.0273 0.00872192.282 kJ>kg4Then the volume flow rate of air into the cooling tower becomesV # 1 m # av 1 196.9 kg>s2 10.842 m 3 >kg2 81.6 m 3 /s(b) The mass flow rate of the required makeup water is determined fromm # makeup m # a 1v 2 v 1 2 196.9 kg>s210.0273 0.00872 1.80 kg/sDiscussion Note that over 98 percent of the cooling water is saved andrecirculated in this case.SUMMARYIn this chapter we discussed the air–water-vapor mixture,which is the most commonly encountered gas–vapor mixturein practice. The air in the atmosphere normally contains somewater vapor, and it is referred to as atmospheric air. By contrast,air that contains no water vapor is called dry air. In thetemperature range encountered in air-conditioning applications,both the dry air and the water vapor can be treated asideal gases. The enthalpy change of dry air during a processcan be determined from¢h dry air c p ¢T 11.005 kJ>kg # °C2 ¢TThe atmospheric air can be treated as an ideal-gas mixturewhose pressure is the sum of the partial pressure of dry air P aand that of the water vapor P v ,P P a P v