Thermodynamics

736 | Thermodynamicsh 1h 3 – h 1ω 1h 1h 3C1Mixing 3section ω 3h 32ω 2h 2h 2Ah 2 – h 3132Dω 2ω 2 – ω 3ω 3ω 3 – ωB 1ω 1Eliminating ṁ a3from the relations above, we obtainm # a 1m # a 2 v 2 v 3v 3 v 1 h 2 h 3h 3 h 1(14–24)This equation has an instructive geometric interpretation on the psychrometricchart. It shows that the ratio of v 2 v 3 to v 3 v 1 is equal to theratio of ṁ a1to ṁ a2. The states that satisfy this condition are indicated by thedashed line AB. The ratio of h 2 h 3 to h 3 h 1 is also equal to the ratio ofṁ a1to ṁ a2, and the states that satisfy this condition are indicated by the dashedline CD. The only state that satisfies both conditions is the intersection pointof these two dashed lines, which is located on the straight line connectingstates 1 and 2. Thus we conclude that when two airstreams at two differentstates (states 1 and 2) are mixed adiabatically, the state of the mixture (state 3)lies on the straight line connecting states 1 and 2 on the psychrometric chart,and the ratio of the distances 2-3 and 3-1 is equal to the ratio of mass flowrates ṁ a1and ṁ a2.The concave nature of the saturation curve and the conclusion above leadto an interesting possibility. When states 1 and 2 are located close to the saturationcurve, the straight line connecting the two states will cross the saturationcurve, and state 3 may lie to the left of the saturation curve. In thiscase, some water will inevitably condense during the mixing process.FIGURE 14–29When two airstreams at states 1 and 2are mixed adiabatically, the state ofthe mixture lies on the straight lineconnecting the two states.EXAMPLE 14–8Mixing of Conditioned Air with Outdoor AirSaturated air leaving the cooling section of an air-conditioning system at14°C at a rate of 50 m 3 /min is mixed adiabatically with the outside air at32°C and 60 percent relative humidity at a rate of 20 m 3 /min. Assuming thatthe mixing process occurs at a pressure of 1 atm, determine the specifichumidity, the relative humidity, the dry-bulb temperature, and the volumeflow rate of the mixture.Solution Conditioned air is mixed with outside air at specified rates. Thespecific and relative humidities, dry-bulb temperature, and the flow rate ofthe mixture are to be determined.Assumptions 1 Steady operating conditions exist. 2 Dry air and water vaporare ideal gases. 3 The kinetic and potential energy changes are negligible.4 The mixing section is adiabatic.Properties The properties of each inlet stream are determined from the psychrometricchart to beh 1 39.4 kJ>kg dry airv 1 0.010 kg H 2 O>kg dry airv 1 0.826 m 3 >kg dry airandh 2 79.0 kJ>kg dry airv 2 0.0182 kg H 2 O>kg dry airv 2 0.889 m 3 >kg dry air