Thermodynamics

cen84959_ch03.qxd 4/14/05 4:09 PM Page 130130 | ThermodynamicsSaturated vaporv gv fSaturated liquid≡v avgSaturatedliquid–vapormixtureto imagine that the two phases are mixed well, forming a homogeneousmixture (Fig. 3–35). Then the properties of this “mixture” will simply bethe average properties of the saturated liquid–vapor mixture under consideration.Here is how it is done.Consider a tank that contains a saturated liquid–vapor mixture. The volumeoccupied by saturated liquid is V f , and the volume occupied by saturatedvapor is V g . The total volume V is the sum of the two:V V f V gV mv ¡ m t v avg m f v f m g v gDividing by m t yieldsm f m t m g ¡ m t v avg 1m t m g 2v f m g v gv avg 11 x2v f xv gFIGURE 3–35A two-phase system can be treated as ahomogeneous mixture for convenience.P or TAx =v avg – v fABACBv fgv f v avgv g vFIGURE 3–36Quality is related to the horizontaldistances on P-v and T-v diagrams.Csince x m g /m t . This relation can also be expressed asv avg v f xv fg 1m 3 >kg2where v fg v g v f . Solving for quality, we obtainx v avg v fv fg(3–4)(3–5)Based on this equation, quality can be related to the horizontal distanceson a P-v or T-v diagram (Fig. 3–36). At a given temperature or pressure, thenumerator of Eq. 3–5 is the distance between the actual state and the saturatedliquid state, and the denominator is the length of the entire horizontalline that connects the saturated liquid and saturated vapor states. A state of50 percent quality lies in the middle of this horizontal line.The analysis given above can be repeated for internal energy and enthalpywith the following results:u avg u f xu fg 1kJ>kg2h avg h f xh fg 1kJ>kg2(3–6)(3–7)All the results are of the same format, and they can be summarized in a singleequation asy avg y f xy fgwhere y is v, u, or h. The subscript “avg” (for “average”) is usually droppedfor simplicity. The values of the average properties of the mixtures arealways between the values of the saturated liquid and the saturated vaporproperties (Fig. 3–37). That is,y f y avg y gFinally, all the saturated-mixture states are located under the saturationcurve, and to analyze saturated mixtures, all we need are saturated liquidand saturated vapor data (Tables A–4 and A–5 in the case of water).