11. Ideal Gas Mixture

Transcription

1 . Ideal Ga xture. Geeral oderato ad xture of Ideal Gae For a geeral xture of N opoet, ea a pure ubtae [kg ] te a for ea opoet. [kol ] te uber of ole for ea opoet. e al a ( ) [kg ] N e al uber of ole ( ) [kol ] for o-reatg ubtae are N

2 e a frato ( ) [kg /kg ] for ea opoet e ole frato (y ) [kol /kol ] for ea opoet y u, N N y e oleular a for ea opoet ( ) [kg /kol ]

3 o oert betwee a ole ba ad a a ba, we a wrte y y y e oleular a for te xture ( x ) [kg /kol ] x y x

4 oder a xture of two gae, we a eaure,, V, of te xture, a well a ad y e Dalto odel Ea opoet beae aordg to te deal ga odel. For te xture, V ad For te opoet, V ad V

5 Fro, we a wrte V V V ad are te partal preure. u, y ad y e preure frato ( /) equal to te opoet ole frato. For te deal-ga xture equato for te a ba, V x x x x x te ga otat for te xture

6 oder a deal-ga xture wt te Dalto odel uder a proe wt otat y. e teral eergy ad te etalpy of a deal-ga xture a be ealuated. u u u u u U H ue otat 0 ad p0 of ea opoet 0,x 0, 0, 0, 0,,,,, u u u u u u p0,x p0, p0, 0,x ad p0,x te pef eat at a otat olue ad a otat preure for te xture.

7 e etropy of a deal-ga xture S y ug a otat p0 odel, te etropy for ea opoet relate to a referee tate 0, 0 ad p0, 0 y l l Wt te aellato 0, 0, 0 ad y, te etropy age for a opoet p0,,, l l e etropy age of te xture p0,,,,,,,,, l l p0, l l

8 p0,x l x l For a etrop proe wt otat properte x p0,x k x kx were k x p0,x / 0, x Note If te opoet properte are treated a otat, te xture properte a be detered by te a/olar aerage etod. e xture wt toe aerage properte (u a x, x, p0,x or K x ) a be treated a a pure ubtae.

9 . Splfed odel of a xture Iolg Gae ad a Vapor oder a deal-ga xture otat wt a old or lqud pae of oe of te opoet. deal-ga xture deal-ga xture wt te aporzed Sold/lqud pae upto No doled gae to old/lqud pae e deal-ga xture ae of gaeou pae Utlzg of te Dalto odel No effet of te deal-ga xture o te equlbru betwee te odeed pae ad t apor

10 exaple of ar ad H O apor ge ere. I geeral, te a frato of H O (wet) atoper ar te outry %. log a te proe doe ot ole te odeato of water apor, te aupto of dry ar applable. oder a xture of dry ar ad H O apor at = a + Dry ar + H O apor wt x a ad x or y a ad y Itally, water apor wt a partal preure ( ) ad teperature () a upereat-apor tate. If t xture ooled dow uder a otat-preure proe, te odeato wll our at te dew- teperature ( pot ). dew

11 dew pot State : Supereat apor at tal tate State : Dew pot State 3: odeato at a otatolue proe e xture a aturated xture we te apor at at ad at. e relate udty () [-] or [%] g t tate 4 at@ or g te aturato preure at te xture teperature (or a te fgure).

12 e udty rato () [-] te rato of te a of water apor to te a of dry ar. ould be alled te pef udty or te abolute udty. e relato betwee ad te a frato of water apor te xture: o r a y ug te deal ga law V / a V / a For a ar-water xture, a a a a Subttute te defto of ge a a

13 ewrtg ter of yeld (0.6 ) e axu udty rato (ax) [-] orrepod to = 00% ax 0.6 t te ae ad, ax. Note tat at a ge, ax = f() oly. Note: roe 3 a obar oolg proe. State te dew pot. Furter oolg lower ax, reultg odeato.

14 .3 e Eergy Equato ppled to Ga-Vapor xture Due to te deal gae xture, te opoet a be treated eparately we alulatg te properte. For a otrol a Q W E E E For a otrol olue d dt E for all ext ( for all let ( V g Z ) Q g Z W e ga g repreet te uato for all opoet te xture. V )

15 .4 e dabat Saturato roe e adabat aturato proe a proe were te ar + HO xture oe dret otat wt water. e proe adabat. e let ar ot aturated, ad oe of water wll eaporate. e ext ar aturated. e ext xture teperature te adabat aturato teperature. e beeft to eaure or of te let ar. e frt law a be redued to a ( ) w a ( w ) pa ( ) fg

16 .5 Egeerg pplato: Wet- ulb ad Dry-ulb eperature ad te yroetr art o eaure te udty of a ar + H O xture, te ple dee alled a pyroeter ued. e dry-bulb teperature ( db ) ply te teperature of te xture. e wet-bulb teperature ( wb ) te teperature eaured fro a teroeter oered wt a otto wk aturated wt water.

17 e adabat aturato teperature ofte alled te terodya wet- bulb teperature. eall te frt law of te adabat aturato proe: ( w ) pa ( ) fg ( ) pa ( ) w For a ge, e = f( ) ad ( or ax@), fg, w = f( ), we olude tat f(, ) f( db fg, Wt t relato, a be alulated fro te eaured db ad wb. Note: For te ae ar, wb alway db. wb = db were te ar aturated. wb )

18 I fat, wb eaured fro te pyroeter loe to te adabat aturato teperature, but ot exatly te ae. Hudty a be eaured by oter eletro dee. For a bary xture, t requre tree depedet properte to fx a tate. pyroetr art ued to fd properte of a ar + H O xture at a ge ( = 00 ka te textbook).

19 e etalpy of a ar + H O xture ge by ~ a 0 Note for te pyroetr art (fro te textbook): fxed at bar wt a orreto fator ae of dfferet. We fxed, two depedet properte are requred to fx a tate of a ar + H O xture db o x-ax, ad o y-ax. For te etalpy of te xture, t aued tat a = 0 kj/kg at 0 o. e etalpy of water apor a be detered by te tea table. e le of otat ~ are alot parallel to te le of otat wb. e ua ofort zoe a be apped o te art o

20 I oter pyroetr art, ~ defed dfferetly: for SHE pyroetr art ~ Se te deal ga aupto wt otat p a be appled a ( a0 kj.006 kg K ( 0 kj,50 kg a pa p ) ) kj.86 kg K Were a0 =0 kj/kg ad 0 =,50 kj/kg at 0 o. u, ~.006 (,50.86 ) ~ kj/kgda ad o.

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22 e dreto for arou proe e ow o te pyroetr art. Note: ~ For adabat aturato proe, alot a otat. e proe fro te oolg proe wtout deudfato (=ot.). e proe fro 3 te oolg proe wt deudfato alog ax le.

23 Exaple of applato te arodtog proee: Deudfato wt reeatg oolg tower

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