Relate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added

Transcription

1 4.3, 4.4

2 Phas Equlbrum Dtrmn th slops of th f lns Rlat p and at qulbrum btwn two phass ts consdr th Gbbs functon dg η + V Appls to a homognous systm An opn systm whr a nw phas may form or a nw componnt can b addd dg η + V G + n j j dn j j Numbr of componnts Numbr of phass

3 dg η G + V + n j j dn j G η Is th chmcal potntal μ G n Chang n th Gbbs functon of th systm wth a chang n th numbr of mols of a gn componnt or phas μ g dg η + V + j μ j dn j constant tmpratur constant prssur On componnt dg μ j dn j j

4 closd systm On componnt 3 phass h numbr of mols of a gn phas can ary undr possbl phas transtons otal numbr of mols n n + n + n3 constant dn 0 For a closd systm at constant tmpratur constant prssur dg μ j dn j j 0

5 Condtons for qulbrum btwn two phass and hrmal qulbrum f Hat would flow from on phas to th othr No qulbrum p p Mchancal qulbrum f p p Chmcal qulbrum On phas would b xpandng at th xpns of th othr μ μ No qulbrum f μ μ A transfr on n mols would chang th Gbbs functon

6 Durng a phas chang hat s addd to (or rmo) from th systm No chang of tmpratur of prssur Enthalpy chang durng th phas transton s Δh atnt hat of th phas n transton atnt hat of fuson atnt hat of aporzaton atnt hat of sublmaton l l l l l h l h h h h h lqud l sold-lqud phas transton lqud-apor phas transton sold-apor phas transton c apor

7 Phas chang procss Constant prssur dh dη + Δh Δη Δh atnt hat molcular ntractons Strong n lqud Wak n a gas Durng aporzaton h majorty of latnt hat s usd to orcom th cohs forcs holdng th molculs togthr n th lqud atnt hat of fuson s much lss than th hat of aporzaton Dnsty dffrnc btwn sold and lqud s rlat small

8 Dtrmn th slops of th f lns μ G G d g dg μ Δη Δh η dg η + dg η + + η + η η Δη Δ Δh Δ Δ Clapyron quaton Frst latnt hat quaton

9 Δ Ealuat th slop f lns Sold-lqud qulbrum ln ( ) Inrtng ( ) l l qud-apor qulbrum ln At th trpl pont l 06 m 3 kg m kg l l Varaton of th mltng pont wth prssur >> l ( ) l l l

10 l If w us th l dal gas law R p Clausus Clapyron quaton h bolng pont tmpratur h tmpratur at whch th apor prssur s qual to th atmosphrc prssur R p l Dcras of bolng pont tmpratur wth dcrasng prssur o ntgrat l ( ) ts assum l constant Watr apor prssur d ( ln ) l R

11 ln l R xp R l Saturaton apor prssur at Rmmbr w assum Vapor phas obys th dal gas l constant Vapor-c qulbrum ln d ( ).09 0 >> m kg d l ntgratng xp R

12 o ntgrat Clausus clapyron quaton mor prcsly Includng th araton of l Wth dδh Δh + Δh p dh c p dδh Δh + Δh p Δc p + Δh p small d l c c Krchoff s law p pl scond latnt hat quaton h araton of th atnt hat of fuson d l c pl c p

13 Consdr a systm ayr of lqud watr orlan by a layr of watr apor Vapor prssur qual to th saturaton apor prssur of th lqud Condnsaton Eaporaton Entropy dcrass ncrass qud s a lss random stat

14 Atmosphrc humdty arabls ast sctons Pur watr apor as th gasous phas undr consdraton In th atmosphr Mxtur of dry ar gass and watr apor Partal prssur of th watr apor Partal prssur of dry ar otal atmosphrc prssur p p d h saturaton apor prssur wth rspct to lqud s h saturaton apor prssur wth rspct to c s

15 Clausus-Clapyron quaton l p R Intgratng th Clausus-Clapyron quaton for atmosphrc watr apor s s, tr xp R l tr saturaton apor prssur wth rspct to lqud s s, tr xp R tr saturaton apor prssur wth rspct to c Rfrnc prssur and tmpratur rpl pont s, tr 6.hPa tr 73.6 K

16 Applcaton of th Clausus-Clapyron quaton to dtrmnng th saturaton apor prssur n th atmosphr s not strctly ald Dalton s law of partal prssurs s not strctly ald h total prssur s not th sum of th partal prssurs of two dal gass h condnsd phas s undr a total prssur that s augmntd by th prsnc of dry ar h condnsd phas s not purly lqud watr, but contans dssold ar Dpartur from dal gas ss than % 7 Whn hgh accuracy s ndd Emprcal alus s a + a n n( tr ) n

17 Valus of saturaton apor prssur Usd to dtrmn commonly usd atmosphrc arabls Rlat humdty H s Partal prssur of th watr apor saturaton apor prssur wth rspct to lqud Rlat humdty wth rspct to c saturaton H s Multpld by 00 prcntag Functon only of If w compar saturaton apor prssur wth rspct to lqud s saturaton apor prssur wth rspct to c s

18 s l s, tr xp R tr s s, tr xp R tr s l tr xp Rtr ( ) ( ) s For subfrzng s > tmpraturs!! Rato ncrass as th tmpratur dcrass s Atmosphr saturatd wth rspct to lqud watr H (C) H Suprsaturatd wth rspct to c

19 Watr mxng rato w Rato of th mass of watr apor prsnt to th mass of dry ar w m ρ ε m ρ p d d ε M M d Saturaton mxng rato w s w s s ε p s q p >> m d m + m p >> s ε p ( ε ) w + w H w q w w s H s Ar always smallr than 0.04 q w Gn,p,and on of th humdty arabl all th othr humdty arabls can b dtrmnd

20 Prcptabl watr Watr apor path W h total mass of watr apor n a column of unt cross-sctonal ara xtndng from th surfac to th top of th atmosphr W ρ dz 0 If all th apor n th column wr to b condnsd th th would b W ρ h rlatonshp btwn prcptabl watr and spcfc humdty W dz ρdz ρg 0 W p 0 g p ρ ρ a q m p 0 W md + m p g q