School of Aerospace Engineering Equilibrium Diagrams and Saturated Liquid/Vapor Systems

Transcription

1 School o Aerospace Enineerin Equilibriu Diaras and Saturated Liquid/Vapor Systes In equilibriu, dierent phases o atter as, liquid, solid (also ultiple solid phases, e.., dierent crystalline structures o steel) So ar looked at indiidual phases o siple (hooeneous) substances Multiple phases can exist siultaneously in equilibriu Consider heatin siple copressible substance at constant pressure Phase Equilbriu and Saturated Liquid/Gas Systes - School o Aerospace Enineerin Phase ransitions - Constant Pressure Start with solid u + Liquid 2 + Liquid 2 Liquid 4 5 Liquid 4 Gas P hi P lo Sall chane in until as 5 Gas P hi P lo F=const Q 2: Meltin 4 5: Eaporation 5 2: Freezin/Fusion 5 4: Condensation Phase Equilbriu and Saturated Liquid/Gas Systes -2

2 School o Aerospace Enineerin ypical - Diara P crit Saturation States = Phase ransitions P hi Gas/ Superheated Vapor Phase Equilbriu and Saturated Liquid/Gas Systes - (Saturated) Vapor Doe + as/apor P low riple Line School o Aerospace Enineerin Phases o Copressible Substances riple Line all phases can coexist at sae and P Critical Point axiu and p at which distinct liquid and as phases can coexist Supercritical States (or supercritical luid) or p>p crit ), no distinct transition ro liquid to as, luid can hae characteristics o both P crit + as/apor Gas/ Superheated Vapor riple Line Phase Equilbriu and Saturated Liquid/Gas Systes -4 2

3 School o Aerospace Enineerin Phase space not just 2 diensional Surace View p =constant P crit Gas/ Superheated Vapor + as/apor Phase Equilbriu and Saturated Liquid/Gas Systes -5 riple Line School o Aerospace Enineerin Independent D properies p and not independent Mixed Phase Reions phase transition at const. p, (e.., ien sat, know p sat ) Can deine new intensitie ariable to characterize coposition describe how uch o each phase present should not depend on total ass Gas/Vapor saturated apor riple Point + as/apor ( sat, p sat ) saturated liquid - = Gas/ Superheated Vapor P sat Critical Point sat p Phase Equilbriu and Saturated Liquid/Gas Systes -6

4 School o Aerospace Enineerin Quality o Saturated Liquid-Vapor For saturated liquid-apor reion (apor doe) new ariable is quality, x x ixture x ies raction o ass that is as () (-x) is raction o ass that is liquid () 0< x < (0 or liquid, or as) apor ass raction, Y liquid ass raction, Y l Phase Equilbriu and Saturated Liquid/Gas Systes -7 Phase Equilbriu and Saturated Liquid/Gas Systes -8 School o Aerospace Enineerin Volue o Saturated Liquid-Vapor Mixture Get D properties o saturated ixture by suin up proper aount o property or each phase, e.., Vix ix ix ix ix x x or ix x ix x - where as, liquid x P saturated liquid Mixture State - = ix saturated apor Gas/Vapor 4

5 School o Aerospace Enineerin Saturated Liquid-Vapor Mixture Properties For eneral intensie property y that obeys su rule, or y y ix ix xy y x x y y with y y - y y ix always bounded by y, y does not work or ( + 2 ) Does ix obey su rule? Phase Equilbriu and Saturated Liquid/Gas Systes -9 School o Aerospace Enineerin Exaple : Gien: k o water at 200C with quality x=0.6 Find: Volue (V) and internal enery (U) Assue: phase equilibriu Phase Equilbriu and Saturated Liquid/Gas Systes -0 5

6 Analysis: Phase Equilbriu and Saturated Liquid/Gas Systes - School o Aerospace Enineerin Exaple : V x able B. k k k k 0.2 U u xu kj k k 569kJ Note: ix >> (~70) because >> or << What is pressure o ixture? = k =200C x=0.6 u only ~u School o Aerospace Enineerin Exaple 2: V=const Gien: 5 lb o water initially at 700F and 2000 psia in riid container Find: How uch enery loss required to cool water to 00F Assue: equilibriu initial and inal state Analysis: p dv=0 Q,p Q U u u 2 Need u 2 and u Phase Equilbriu and Saturated Liquid/Gas Systes -2 6

7 School o Aerospace Enineerin Exaple 2: V=const =700F p =2000psi =5 lb Q u =? > sat superheated apor u =47.2 BU/lb Phase Equilbriu and Saturated Liquid/Gas Systes - School o Aerospace Enineerin Exaple 2: V=const 2 =00F 2 =0.249t /lb =5 lb Q < 2 < saturated ixture 2 2 x2 x u u x u 299 BU lb 2 2 Phase Equilbriu and Saturated Liquid/Gas Systes -4 U u u2 Q 5lb BU lb 4240BU 4.47MJ 7

8 P School o Aerospace Enineerin Exaple 2: Gas/Vapor V=const =700F p =2000psi =0.25t /lb =5 lb 2 =00F p 2 =66.97psi 2 =0.25t /lb =5 lb 2 Do phases always coexist in equilibriu? Phase Equilbriu and Saturated Liquid/Gas Systes -5 8