Thermodynamics

240 | Thermodynamicsu 1 = 94.79 kJ/kgP 1 v 1 = 0.68 kJ/kg(h 1 = 95.47 kJ/kg)Throttlingvalveu 2 = 88.79 kJ/kgP 2 v 2 = 6.68 kJ/kg(h 2 = 95.47 kJ/kg)FIGURE 5–31During a throttling process, theenthalpy (flow energy internalenergy) of a fluid remains constant.But internal and flow energies may beconverted to each other.Assumptions 1 Heat transfer from the tube is negligible. 2 Kinetic energychange of the refrigerant is negligible.Analysis A capillary tube is a simple flow-restricting device that is commonlyused in refrigeration applications to cause a large pressure drop in the refrigerant.Flow through a capillary tube is a throttling process; thus, the enthalpyof the refrigerant remains constant (Fig. 5–31).At inlet:At exit:P 1 0.8 MPaf T 1 T sat @ 0.8 MPa 31.31Csat. liquid h 1 h f @ 0.8 MPa 95.47 kJ/kg(Table A–12)P 2 0.12 MPa ¡ h f 22.49 kJ/kg T sat 22.32C(h 2 h 1 ) h g 236.97 kJ/kgObviously h f h 2 h g ; thus, the refrigerant exists as a saturated mixture atthe exit state. The quality at this state isx 2 h 2 h f 95.47 22.49h fg 236.97 22.49 0.340Since the exit state is a saturated mixture at 0.12 MPa, the exit temperaturemust be the saturation temperature at this pressure, which is 22.32°C.Then the temperature change for this process becomes¢T T 2 T 1 122.32 31.312°C 53.63°CDiscussion Note that the temperature of the refrigerant drops by 53.63°Cduring this throttling process. Also note that 34.0 percent of the refrigerantvaporizes during this throttling process, and the energy needed to vaporizethis refrigerant is absorbed from the refrigerant itself.HotwaterT-elbowColdwaterFIGURE 5–32The T-elbow of an ordinary showerserves as the mixing chamber for thehot- and the cold-water streams.4aMixing ChambersIn engineering applications, mixing two streams of fluids is not a rareoccurrence. The section where the mixing process takes place is commonlyreferred to as a mixing chamber. The mixing chamber does not have to bea distinct “chamber.” An ordinary T-elbow or a Y-elbow in a shower, forexample, serves as the mixing chamber for the cold- and hot-water streams(Fig. 5–32).The conservation of mass principle for a mixing chamber requires that thesum of the incoming mass flow rates equal the mass flow rate of the outgoingmixture.Mixing chambers are usually well insulated (q 0) and usually do notinvolve any kind of work (w 0). Also, the kinetic and potential energiesof the fluid streams are usually negligible (ke 0, pe 0). Then all thereis left in the energy equation is the total energies of the incoming streamsand the outgoing mixture. The conservation of energy principle requires thatthese two equal each other. Therefore, the conservation of energy equationbecomes analogous to the conservation of mass equation for this case.