Thermodynamics

cen84959_ch03.qxd 4/1/05 12:31 PM Page 153Chapter 3 | 153SUMMARYA substance that has a fixed chemical composition throughoutis called a pure substance. A pure substance exists in differentphases depending on its energy level. In the liquidphase, a substance that is not about to vaporize is called acompressed or subcooled liquid. In the gas phase, a substancethat is not about to condense is called a superheated vapor.During a phase-change process, the temperature and pressureof a pure substance are dependent properties. At a given pressure,a substance changes phase at a fixed temperature, calledthe saturation temperature. Likewise, at a given temperature,the pressure at which a substance changes phase is called thesaturation pressure. During a boiling process, both the liquidand the vapor phases coexist in equilibrium, and under thiscondition the liquid is called saturated liquid and the vaporsaturated vapor.In a saturated liquid–vapor mixture, the mass fraction ofvapor is called the quality and is expressed asx m vaporm totalQuality may have values between 0 (saturated liquid) and 1(saturated vapor). It has no meaning in the compressed liquidor superheated vapor regions. In the saturated mixture region,the average value of any intensive property y is determinedfromy y f xy fgwhere f stands for saturated liquid and g for saturated vapor.In the absence of compressed liquid data, a general approximationis to treat a compressed liquid as a saturated liquid atthe given temperature,y y f @ Twhere y stands for v, u, or h.The state beyond which there is no distinct vaporizationprocess is called the critical point. At supercritical pressures,a substance gradually and uniformly expands from the liquidto vapor phase. All three phases of a substance coexist inequilibrium at states along the triple line characterized bytriple-line temperature and pressure. The compressed liquidhas lower v, u, and h values than the saturated liquid at thesame T or P. Likewise, superheated vapor has higher v, u,and h values than the saturated vapor at the same T or P.Any relation among the pressure, temperature, and specificvolume of a substance is called an equation of state. The simplestand best-known equation of state is the ideal-gas equationof state, given asPv RTwhere R is the gas constant. Caution should be exercised inusing this relation since an ideal gas is a fictitious substance.Real gases exhibit ideal-gas behavior at relatively low pressuresand high temperatures.The deviation from ideal-gas behavior can be properlyaccounted for by using the compressibility factor Z, definedasThe Z factor is approximately the same for all gases at thesame reduced temperature and reduced pressure, which aredefined aswhere P cr and T cr are the critical pressure and temperature,respectively. This is known as the principle of correspondingstates. When either P or T is unknown, it can be determinedfrom the compressibility chart with the help of the pseudoreducedspecific volume, defined asThe P-v-T behavior of substances can be represented moreaccurately by more complex equations of state. Three of thebest known arevan der Waals:whereBeattie-Bridgeman:whereBenedict-Webb-Rubin:P R uTv a B 0R u T A 0 C 0T b 1 2 v bR uT a aa2 v 3 v 6Z PvRT orZ v actualv idealT R T T crandP R P P cra 27R2 2T crandb RT cr64P cr8P crA A 0 a 1 a v bandB B 0 a 1 b v bcv 3 T a 1 g2 v b 2 eg>v2v actualv R RT cr >P cra P a b1v b2 RT2vP R uTv a 1 c2 v T b1v B2 A 3 v 2where R u is the universal gas constant and v – is the molar specificvolume.