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1 t. essue cectns f stndd ml themdynmc ppetes f cndensed substnces nd fluds usn dt fm DCmp ecds f GEM-elekt.. essue cectns t cndensed substnces fte cectn fm efeence tempetue ( usully. K) t tempetue f nteest the ml themdynmc functns f substnces cn be cected fm efeence pessue (usully b) t elevted pessue f nteest usn the stndd ml vlume. t mdete pessues nd tempetues (- C) ml vlumes f slds nd lquds cn be ssumed cnstnt. hs leds t the fllwn smple cectns: ; ; ; (-bc) t hhe tempetues nd pessues b (when - ) ml vlumes f cndensed substnces e n lne cnstnt. hee e sevel wys t descbe the theml expnsn nd the cmpessblty f mnels melts nd lqud wte. ccdn t Dkupets et l. (988) the dependence f ml vlume n nd t b ( - ) s tken n the fllwn fm: (-). he bve equtn becmes equvlent t tht ven by emn (988) fte settn. Usn eqn (-) the ml Gbbs eney functn t nd cn be btned s: [ d (-). he ml entpy t nd b cn be clculted s: [ d (-) nd the ml enthlpy functn s: [ d (-). hese clcultns e mplemented n elekt cdes snce 988. Fm eqn (-) ceffcents f theml expnsn α nd cmpessblty β cn be evluted s:
2 . essue cectns f DCmp themdynmc dt v.. (peped by D.Kulk & h.ne) α (-6); β (-7). Usn theml expnsn nd cmpessblty ceffcents nd ssumn tht bth e cnstnt the ml vlume t cn be ltentvely clculted s: [ β α (-8). ltentvely nsted f the empcl eqn (-) the ppxmte eqn (-8) ne cn cnsde usn tempetue-dependent sbc theml expnsn nd cmpessblty s suested by Hllnd nd well (998). hey defned the theml expnsn ceffcent s: α (-9) whee the nput pmete s lmtn theml expnsn vlue t hh tempetues. hs ves the fllwn tempetue cectn f the stndd ml vlume: [ (-). Cmpessblty f sld phses s functn f pessue s hndled usn the Munhn equtn f stte (E): (-) whee s the bulk mdulus (n unts f pessue) nd s the pessue devtve f the bulk mdulus. Upn enn ne btns: (-) whee s ven n eqn (-) nd. [ (Hllnd nd well 998). lues f nd shuld be tken n kb n eqns (-) t (-) nd (-). hs esults n the fllwn expessn f the ml Gbbs eney t : [ d (-).
3 It fllws fm eqn (-) nd the defntn α tht the ml entpy t s: d (-) F the ml enthlpy functn t ne then clcultes: G [ (-). ltentve pessue cectns (usn dffeent ppxmtn f the ch-munhn E nd dffeent fm f theml expnsn) e mplemented f the dt fm M. Gttschlk s dtbse (Gttschlk 997) mpted nt GEM-elekt DCmp fmt (t be descbed n septe dcument)... essue cectns t queus nnelectlytes thuh ppetes f tn he mst cmmnly used ppch f clcultn the stndd stte themdynmc ppetes f queus speces t elevted tempetues nd pessues pples the evsed Helesn- Kkhm-Flwes (HKF) equtn f stte (ne nd Helesn 988). hs mdel ws nlly develped f ched queus speces nd ts extensn t queus nnelectlyte speces (hck nd Helesn 989) enelly lcks us theetcl bss. Cnsequently pplctn f ths mdel t queus nnelectlytes fces ntnsc lmttns. he pefmnce f the HKF mdel t supectcl cndtns nd n the ne-ctcl en f wte s nt vey d whch hs esulted n nn effts t develp me dequte equtns f stte f queus nnelectlytes (lysunv et l. ; b; edlbue et l. ; knfev nd Dmnd ). hese mdels e ll bsed n the Gbbs eney (nd the ppetes) f tn f queus speces whch s defned s fllws: G G G (-6) whee G s the Gbbs eney f the queus slute n the del s stte nd G s the Gbbs eney f tn. hs ccunts f the tnsfe f the queus slute fm the del s stte t the slvted queus speces. ll the ptl mll ppetes f the queus speces e clculted thuh sttements nlus t eq. (-6). he nly exceptn s the ptl mll vlume f speces whch s clculted dectly fm the equtn f stte wthut efeence t the vlumetc ppetes f the del s. he knfev-dmnd mdel f queus nnelectlytes ws mplemented nt GEM-elekt s specl cse f pessue cectn. he mll themdynmc ppetes f the speces n the del s stte e clculted thuh stndd het cpcty ntetn nd the tn ppetes e then dded s pessue cectn. he Gbbs eney f tn s clculted s (knfev nd Dmnd ):
4 G R ln N R HO ( ξ) b R ln f. HO R ξ ln R M w HO (-7) Hee N s the numbe f mles H O n k (.) fho s the stndd stte fucty f H O HO s wte densty R s equl t 8.. he pmetes b nd ξ e empcl ceffcents f the E mdel. he ptl mll vlume entpy nd het cpcty e clculted s (knfev nd Dmnd ):. HO ξ ξ HO R R HO b (-8) HO ( ξ)( ) HO R HO HO b R ln N. R ξ ξln R M ξln HO ξ HO HO (-9) Cp ( ξ)( Cp Cp ) R HO HO HO R ξ ξ. b HO HO ξ ( ) HO HO ξ (-) HO HO lutns f the ptl devtves ven n eqs. (-8) (-9) nd (-) e ven n knfev nd Dmnd (). he enthlpy f tn s btned fm the stndd eltnshp: G H G (-) he mdel eques the del s ppetes f the queus slute nd thee empcl pmetes whch e vlble f numbe f cmmn slutes such s CO (q) H (q) O (q) nd H (q). hese empcl pmetes cn ls be estmted fm stndd stte ppetes t nd usn celtn equtns fm (knfev nd Dmnd ).. essue cectns f DCmp themdynmc dt v.. (peped by D.Kulk & h.ne)
5 Refeences knfev N.N. Dmnd L.. () hemdynmc descptn f queus nnelectlytes t nfnte dlutn ve wde ne f stte pmetes. Gechm. Csmchm. ct emn R.G. (988) Intenlly cnsstent themdynmc dt f mnels n the system N O-K O- CO-MO-FeO-Fe O -l O -O -O -H O-CO. Junl f etly 9 -. Dkupets.I. Kpv I.K. Lshkevch.. Nebue.. Kzmn L.. (988) Isbcstheml ptentls f mnels ses nd queus speces n the elekt pm pcke. In: hyscchemcl mdels n echemsty (eds. Kselev.I. nd Kpv I.K.) Nuk ubl. Nvsbsk p. -7 (n Russn). Hllnd.J.. well R. (998) n ntenlly cnsstent themdynmc dt set f phses f petlcl nteest. Junl f Metmphc Gely Gttschlk M. (997) Intenlly cnsstent themdynmc dt f ck-fmn mnels n the system O -O -l O -Fe O -CO-MO-FeO-K O-N O-H O-CO. Eu. J. Mnel lysunv.. O Cnnell J.. d R.H. () Infnte dlutn ptl ml ppetes f queus slutns f nnelectlytes. I. Equtns f ptl ml vlumes t nfnte dlutn nd stndd themdynmc functns f tn f vltle nnelectlytes ve wde nes f cndtns. Gechm. Csmchm. ct lysunv.. O Cnnell J.. d R.H. hck E.H. (b) Infnte dlutn ptl ml ppetes f queus slutns f nnelectlytes. II. Equtns f stndd themdynmc functns f tn f vltle nnelectlytes ve wde nes f cndtns ncludn the subctcl tempetues. Gechm. Csmchm. ct edlbue J. O Cnnell J.. d R.H. () new equtn f stte f celtn nd pedctn f stndd mll ppetes f queus electlytes nd nnelectlytes t hh tempetues nd pessues. Chem. Gel hck E.L. Helesn H.C. (989) Clcultn f the themdynmc ppetes f queus speces t hh pessues nd tempetues: tndd ptl mll ppetes f nnc neutl speces. Gechm. Csmchm. ct 7-8. ne J.C.I. Helesn H.C. (988) Clcultn f the themdynmc nd tnspt ppetes f queus speces t hh pessues nd tempetues: Revsed equtns f stte f stndd ptl mll ppetes f ns nd electlytes. me. J. c
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