Thermodynamics

cen84959_ch03.qxd 4/1/05 12:31 PM Page 129x m vaporm total(3–3)Chapter 3 | 129is the difference between v g and v f . Reading these values from Table A–5 atP, kPa100 kPa and substituting yieldv fg v g v f 1.6941 0.001043 1.6931 m 3 >kgThus,Sat. liquid Sat. vapor¢V mv fg 10.2 kg2 11.6931 m 3 >kg2 0.3386 m 3P = 100 kPa P = 100 kPa(b) The amount of energy needed to vaporize a unit mass of a substance at agiven pressure is the enthalpy of vaporization at that pressure, which is h fg 2257.5 kJ/kg for water at 100 kPa. Thus, the amount of energy transferred ismh fg 10.2 kg212257.5 kJ>kg2 451.5 kJ100Discussion Note that we have considered the first four decimal digits of v fgand disregarded the rest. This is because v g has significant numbers to thefirst four decimal places only, and we do not know the numbers in the otherv f v g vdecimal places. Copying all the digits from the calculator would mean thatwe are assuming v g 1.694100, which is not necessarily the case. It could FIGURE 3–33very well be that v g 1.694138 since this number, too, would truncate to Schematic and P-v diagram for1.6941. All the digits in our result (1.6931) are significant. But if we did Example 3–3.not truncate the result, we would obtain v fg 1.693057, which falselyimplies that our result is accurate to the sixth decimal place.1b Saturated Liquid–Vapor MixtureDuring a vaporization process, a substance exists as part liquid and partvapor. That is, it is a mixture of saturated liquid and saturated vapor(Fig. 3–34). To analyze this mixture properly, we need to know the proportionsof the liquid and vapor phases in the mixture. This is done by definingP or Ta new property called the quality x as the ratio of the mass of vapor to theCritical pointtotal mass of the mixture:wherem total m liquid m vapor m f m gQuality has significance for saturated mixtures only. It has no meaning inthe compressed liquid or superheated vapor regions. Its value is between 0and 1. The quality of a system that consists of saturated liquid is 0 (or 0percent), and the quality of a system consisting of saturated vapor is 1 (or100 percent). In saturated mixtures, quality can serve as one of the twoindependent intensive properties needed to describe a state. Note that theproperties of the saturated liquid are the same whether it exists alone or ina mixture with saturated vapor. During the vaporization process, only theamount of saturated liquid changes, not its properties. The same can be saidabout a saturated vapor.A saturated mixture can be treated as a combination of two subsystems:the saturated liquid and the saturated vapor. However, the amount of massfor each phase is usually not known. Therefore, it is often more convenientstatesSaturated liquidSat. vaporSat. liquidSaturated vapor statesFIGURE 3–34The relative amounts of liquid andvapor phases in a saturated mixture arespecified by the quality x.v