Chapter 12 Lyes KADEM [Thermodynamics II] 2007

Transcription

1 Chapter 2 Lyes KDEM [Therodynacs II] 2007 Gas Mxtures In ths chapter we wll develop ethods for deternng therodynac propertes of a xture n order to apply the frst law to systes nvolvng xtures. Ths wll be an essental step to understand checal reactons and cobuston. The objectve of ths part s, therefore, to answer to ths sple queston: If I gve you the propertes of a coponent and the propertes of a coponent, what wll be the propertes of the xture +. The frst soluton to answer to ths queston wll be to defne a table of therodynac propertes for each xture. ut obvously, ths s not achevable snce the nuber of cobnatons s endless. It wll be uch easer to deterne the propertes of the xture usng the propertes of each coponent. For that, we need to now the coposton of the xture, as well as, the propertes of the ndvdual coponents. Let us start by soe defntons: The total ass of the xture: C The ole nuber of a xture: + + C +... The ole fracton ole nuber of a coponent ole nuber of the xture Mole fracton y ote that, therefore: y y The ass fracton The ass of a coponent The ass of the xture ote that, Mass fracton f f therefore The olecular weght of the xture can be obtaned as: f M M ym Gas Mxtures 53

2 Chapter 2 Lyes KDEM [Therodynacs II] 2007 nd the xture gas constant wll be: R R U where R U s the unversal gas constant (8.34 J/ol K). M When perforng an analyss on a xture t s portant to state f the analyss s based on the ass [gravetrc analyss] or on the ole nubers or volue [voluetrc analyss] Exaple Molar analyss of ar ndcates that t s coposed prarly of ntrogen (78%) and oxygen (22%). Deterne: - The ole fractons. - The gravetrc analyss. - Its olecular weght. - Its gas constant. -v-t behavor of gas xtures or deal gas-low for xtures: Two odels are used to obtan the -v-t relaton for a xture of deal gases: The agat s odel: In ths odel each coponent s consdered, as t exsts separately at the sae pressure and teperature of the xture. The total volue s the su of the volue of each coponent. agat s odel sae T and For the xture (+) V V For coponent V For coponent ut + V / V / Therefore for the agat s odel: V The general for s: V V V and V are the partal volues. ( ) T, V / + V +V The Dalton s odel: n ths odel each coponent occupes the sae volue and has the sae teperature of the xture. The total pressure s the su of the coponent pressures (partal pressures). Dalton s odel sae T and V V For the xture (+) V For coponent V For coponent Gas Mxtures 54

3 Chapter 2 Lyes KDEM [Therodynacs II] 2007 ut V + V V Therefore for the Dalton s odel: + The general for s: ( T, V ) and are the partal pressures. We can show that, y and y Exaple rgd tan contans 2 g of 2 and 4 g of CO 2 at a teperature of 25 C and 2 Ma. Deterne: - The partal pressures of the two gases. - The gas constant of the xture. ropertes of xtures of deal gases The extensve propertes of a xture, such as H, U and S can be found by sply addng the contrbuton of each coponent, for exaple for enthalpy: H H H... H + + In ter of specfc enthalpy h: H h h Therefore, h h f Ths can be also expressed on a olar bass So n general for: H h h h y h Gas Mxtures 55

4 Chapter 2 Lyes KDEM [Therodynacs II] 2007 u h f f ( Cp) ( C ) s v u h s f f f C C p v Exaple xture s coposed of 2 ol CO 2 and 4 ol 2. It s copressed sentropcally n a cylnder fro 00 a and 20 C to 2 Ma. ssung constant specfc heats. Calculate: - The fnal teperature. - The wor requred. - The change n entropy. John Dalton Englsh eteorologst who swtched to chestry when he saw the applcatons for chestry of hs deas about the atosphere. He proposed the toc Theory n 803 whch stated that () all atter was coposed of sall ndvsble partcles tered atos, (2) atos of a gven eleent possess unque characterstcs and weght, and (3) three types of atos exst: sple (eleents), copound (sple olecules), and coplex (coplex olecules). Dalton's theory was presented n ew Syste of Checal hlosophy ( ). Ths wor dentfed checal eleents as a specfc type of ato, therefore rejectng ewton's theory of checal affntes. Instead, Dalton nferred proportons of eleents n copounds by tang ratos of the weghts of reactants, settng the atoc weght of hydrogen to be dentcally one. Followng Rchter, he proposed that checal eleents cobne n ntegral ratos. Despte the portance of the wor as the frst vew of atos as physcally real enttes and ntroducton of a syste of checal sybols, ew Syste of Checal hlosophy devoted alost as uch space to the calorc theory as to atos. Fgure.0.. John Dalton. Gas Mxtures 56

5 Chapter 2 Lyes KDEM [Therodynacs II] 2007 Mxture of real Gases Dalton s law and agat s law can also be appled to real gases (non-deal gases) wth a reasonable accuracy. However, the devaton fro the deal gas law ust be taen nto account by: - Usng ore approprate (and coplex ) relatons for a real gas. 2- Usng the copressblty factor (Z) V ZR T For a xture, Z can be coputed as: Reeber that: U Z yz ole nuber of a coponent y ole nuber of the xture The proble wth usng the copressblty factor s that ths approach consders only the nfluence of le olecules on each other, neglectng the effect of the olecules of the coponent on the olecules of the coponent. In practce, the predcted values usng the approach of the copressblty factor, aybe far fro the experentally deterned values. The soluton? Kay s rule nother ore accurate approach to predct the behavor of a real gas s to use the Kay s rule (For W.. Kay 963). For that, pseudo crtcal pressure and pseudo crtcal teperature have to be coputed. Then, the copressblty factor wll be deterned usng the elson-obert generalzed copressblty chart (chart page 868 [Cengel s boo]). seudo pressure: ' cr, ycr, ' seudo teperature: T y T cr,i s the crtcal pressure for each coponent of the xture. cr, cr, cr,i s the crtcal teperature for each coponent of the xture. Fro (table., page 824 [Cengel s boo]) The results obtaned by usng Kay s rule s accurate to wthn 0% over a wde range of teperatures and pressures. Ths accuracy s acceptable for ost engneerng purposes. Exaple n nsulated rgd tan of volue contans 0.25 ol of O 2 and 0.4 ol of CO 2 at 300 K. Deterne the pressure of the xture usng: a/ the deal-gas equaton of state. b/ copressblty factors based on Dalton s odel. c/ copressblty factors based on agat s odel d/ Kay s rule. Gas Mxtures 57

6 Chapter 2 Lyes KDEM [Therodynacs II] 2007 ropertes of real gas xtures The study of the propertes of real gas xtures aybe very coplex and counterntutve. To llustrate ths, let us see the followng exaple (Cengel boo page 645). Real gas 25 C a Real gas 25 C a Real gas + 25 C 3 02 a Fgure.0.2. Mxture of real gases. Whle the pressure of both coponents s 00 a, the pressure of the xture s 02 a. Ths ay be explaned by the nfluence of the olecules of dfferent gases on each other. Even though, several approaches exst to deterne the propertes of real gas xtures, the easest way s to use the Kay s rule ( once agan). Exaple r s a xture of 2, O 2 and a sall aounts of other gases, and t can be approxated as 79 percent 2 and 2 O 2 on a ole bass. Durng a steady flow process, ar s cooled fro 220 to 60 K at a constant pressure of 0 Ma. Deterne the heat transfer durng ths process per ol of ar, usng the Kay s rule. Gas Mxtures 58