Pandey, J D

Prajapati, S R

IACS Institutional Repository

lndia,n J. PhY8. 54B. 490-496 (1980) Calculation of thermal conductivities of two binary gas mixtures J D Pandey Dcpltrt,l:llont o( ChOIUll:01t,ry. Umv(muty 04: Allahabad. AlJahalJad and S R Pmjapllti* DOp!l1't.men1, of Chemu~tI'Y, K. N. GyallpUl', Vfuana~i G (}VAl'll.ll10nt Poot ·Grll<1uat,o . €ollogo. R(lc()lvm\ J 8 April l07g 1\ Abstract: The nltcl'na1,ivn proneuures HI'O pl'opol':loll for tho cn.1cnlat.ion uf th~rmal (~ondll('tivlt,icfi of biHary gn.A nuxtUl'NI and Rpplip,d f,\ NSI~N20 and O~-N20 at five tcmporat.ul'(-,R. Th(~ {'htmrf'1 iCIlI vlllufiiR iUP f'onl1\,ed wlth the oxporunt.'lIltal vo.lneR. . 1. Introduction Lindsay and Bromloy (1950) propoR·.1d t,he mHthml for t.he calcmlIMt ion ofWl;B~ilj('wa cooHic'iontR of Wn.~~iIj(lWa oquat.iou (WaRsiljowa 1904) to! MIl' tn"J'TIldl cO/ildllcti· vil,cs of binary !!IIA mixlll'l""s, Ma80ll and Raxom, (1!l5R) "Iso proposed anoiJler method t.o estJm;);t,p, WiI"Rilj( wa eooflh.J(lnLR fot' t.)w ~anoc purp()~". In 'both t,h('~( met.\lOcls, t,ho visrosit.i"" Ill' 1""'<' !I"'~ wmpol1e,.i, (t]'(' rrq;llnd 'Vj~holl1' t,\wil' knowkrlgo t,11O cll,]culation L f Wu",il,jewa (lc'effioi<'nl., is llnt p(lHRibk In uno present. lJal>cr ~,IJ{' aIt.crn~tiv(' procecluwK \h~,\,(' Il('~n HUggt'storl "" (lRt.imat,o WaARlljowa cncffil'inut." fur thermal (lomlunt"vlt,ws of binmx gas mixt,UJ'('s anrl applied 1,(1 N,-NP and 02-N20 using Hirsrhfeldm Euolwn o,pproximn,tJOl1 and Linctslt,I'-Bromley or MaAcm-Raxnna mothod Thl' theol'llt.ieal yahWH IlI'{' cnJUparcd wit,h tho OXpCI inocntal values (l'el'O'J'a. and Haw 1 !l(i3). 'flte mr,rlifi,'d (,XPI'''RSiollfi of' LUldHllY-B/'Olllloy I10wl MIt14011·Raxnna ml'j,h()(b .. liminat (' tho "'IHOnStty to,'JUS of gas component,s. 2. Theory Was~i\Jowa equat.iou (Wa_sillewa I!1041 Imvo hili'll sncoesRf'nlJy ut.iliz('d fOJ t,\w t.hnnnal condueL, vitwA of binary glLR mixt,\II'oR ana it. may ho writ,t.on a~, 490 .. Present addreSR; I)epartment of ChemiRtry. Government, Degree College. Haminpur (D. P) (I) Oalculation of thermal conductivitie8 491 whl'lre " and ". aro the thermal conductivities of t,he mixture and the pure ga.s component i; :v, iR tho U10lA fraotion of ('omponpnt i and All is one two Ret~ of WIIoBSiljcWII coefficienl,H, Cowling et al (1963). Cnwling \1961) and Wright and Gray (1962) havc Ruggestcd the importance of All' Two diffol'llllt theorllticilol aopP"oximatioIlB for WIIHsiljowao c(officient All of Wo.ssiljewa equation have aolreaody oolln ~uggeated. Oue of Ihem is a semI-empirical equation du~ to Lin(tRIIY !loud Bromley (1950), (2) where 1/1, 1/: and MI. Ml are )'esportivcly tho vi~ooBitipB and moleculilor weightH of Cllmp(ll1ll11t4 i, J, fI;; Huth''''land'ij COII"("mt and S" = (SI, Sl)t WhOll th" buth gaRBs are nonpolar, as considol'l,d here. Annther IlopproxiJ1lllotion fOi' W'aosHiljcwllo Ilocfficilm1,R obtainod froJll rigorous thoory haH lIul!ll derivo(l by Masoll Imd Sa.xell8o (19G8), . ( M, )-1 [ (1/1)1 I Jlf j )'/4]2 All = (J·37615 1+ M; 1-1 ~i \ Alj (3) Hirschfddl'r and Ennkell (1964) ha."" grl"on till' fir~t a.pprox)ma.(.ioll to t.hl" thllrnml conductlvit.y of pnro p"lyal,omi(' glL~ tnking into approxillmtoly t,he 1,rlLnRftlr IIf onl"l'gy bet.woon 1.l'ansla.t.lOnaJ and intorIl!lo1 ilogrt'cs of frAcilom in mnloculos. TIll' approximation rl"ln.t.l<H 1,111" t,h(!rml~1 I"ondud.ivit,y 1,(1 (,Ill' vis(losity in l.ho following WILY, (4) whore 11 ami Ova", u]I)\lw 1\1\.,. «llUR1.nu1 ~1lI1 ))l!Jior IlIm1. ca.l""OIt.y a1. COllRtmlt, volumo rllijpect,ivoly For bet.ter valuo~, tho higlwl' 1,lurd n.pproximllotilln (Hll'schfl']ucl' rot a11964) to \,ho COOffiCII.lIl(, lIf (,hermit] conductivlt.y lulVo beOIl t,n]wn a.nd iR l'oprcHcIlt~d a.s fo1l0WH, (5) The approximlltion factors r~j !lond .f"~1 are very <lloea to unity (Hirscbfoldet· et al1964). Henoe the approximo.tion!\,/fsAf::::: 1 may bo adopted. 492 J D PandfIJJ and S R Prajapati It ma.y be noticed (Hirsohfelder et al 1964) that the order of [,(']I/['\IJ1, [Ad. I [All. and A,I AI is the same and the order of ['l/I]I/[71lh and '1/1/'1/1 is also the Barno. Therefore the following arbitrary approximations may be taken UB, (6) With the help of equations (5) and (6), equations (2) and (3) can be trans-formed as, and Equations (7) and (8) are Repal'lIteJy used li)r tho calculation of WaBsiljflwa coefficients and hence for I.he prediClt,ion of tiltH'nm) ennductlvit.ips Tlw relat.ion for molal' heat eapacil.y at constant prOBsme, Gp , (9) whllre Ct, fl, Y and II are constants (GlaHRtonc 1974) dPpeudl'nt. upon the nature of j,he gas, flIlahJes us to calculato tho 01" G" of N •. 0 •. N.O can be calculated from the knowledge of G'P from equation (9) and t.hl' diifeJ'l'ncc of 0'1 and Go (Chapman and Cowling 1970). The observed values of thormal conductivitil's of gas compouonts at differonL temperatures are taken (Peroira and Haw 1963) and the Suthorland's conRt,a.nts nRNl illl>qnaj.icm (7) from t.he \it.oral.llra (Clw.pman a.nd Cowling 1970). The experimental (Pereira and Raw 196:J) and the t,heoretical values of thermal conductivities N,-N20 and 02-N20 at variouR composit.ions and temperatures are represontod in TableR ) and 2 respeotively and Wassiljewa coefficients in Table 3. OaZculation of thermal ooniluctivitie8 493 T.ble 1, Thermal oOncluctlvit,y (Cal Inn-I '"'0-' der) of nitrogen-nitrou. ollide mixtw'<'S fW q. function uf tOlDperatulo. Tem~er .. turo Mole [r"",tion E"pti' Fl'OlQOqUlL. FromeqUR- From aqua- Fromcqua-C ~, LlOns (1) tlO .... (1) tID .... (I) .. tlOns (I) ond (2) ""d (7) and (3) and (S) ). ). ). 31.85 0.234 4.tiD 4 DB 4 Oli 4.78 ~ 7M 0,242 4,73 4114 4,117 4,78 4.711 0.438 4,75 5.28 fi 31 5 04 5.06 (l,/iD2 5.26 Ji 55 5.59 r..30 5,32 0.S58 ro.77 0.0r. II 07 ::; 00 0.91 MOIlII absoluto devw.tion (0 22) (6,77) (2 (2) (2.66) 50 or. (l,17l1 494 5.01 a 02 489 4,90 0.254 4 96 Ii 15 0.111 " 09 4.99 0.309 4 97 5,41 542 5 19 5.19 o 747 r. 44 6.07 608 5.85 5.80 MaanBb8olm.o dovJ.O.tlon (6 ~2) (0 61) (8.39) (3,39) 101.0 0.224 0.16 6,11 0.12 5.95 /i,95 o 301 6,29 6,22 0,24 602 0.03 o 490 6,20 0.59 o IlS 6.26 6.28 0, MY 6.46 6 62 6.64 6 S5 6 37 0.709 6,72 7,01 7,03 0.81 0.82 MeBn "baoluio devja.tlon (2.54) (2.59) (2,24) (2.12) 140.2 o 300 6,(0 6,75 6.77 6,53 0.55 o 439 0,58 0.96 6.98 0.68 6,70 0615 6.47 7 22 7 24 6,93 6.UG 0.803 7 30 7.60 7.62 7.29 7.30 Me .... absolute de"i8tion (6.40) (6.69) (2.70) (2.90) 180.1 0.230 7,18 7 41 7.43 7.23 7,28 0,358 7,29 7 58 7,61 7.34 7.S6 0.4.7. 7 58 7.76 7.70 7.47 7,4.9 11.602 7.50 7.95 7,98 7.65 7.07 0.752 8 23 8.18 820 7.93 7,OG MeBn "bBolute devia.tion (3.23) (S.'8) (1. 70) (1.68) t· .xporilIlentai "aluea are taken (PCIl'8irB aDd Raw 1988) 494 J D Pandey and S R Prajapati Table 2. '.l'hel"lDI11 cOIlrluotlvlty (oBI lcm-1 ,"/oc-1 dog~:l) of ox-ygen-uunrous mwJo mu::tul'OoS u.s a funcLion of t01llpel'a.tuI'O. -------------.....-.--.--Tl'JtnplJl·t1tU1'l"~ Molo n'(l.otlOl1. J!)xptl'" Frunt equu.- r.('l'Ull1 equfl,- From eqUl\- FrOln uqUtl.-·0 ,t', ilOlJa (1) tiona (1) hono(l) 1"Yll. (1) and (~) and (7) and (3) and (8) ,\ " ,\ A 31. 85 0.275 4.0il 5.02 5.04 ·L~H 4.87 0,456 5.43 G 30 r. :18 5.13 0.15 o 669 [j 55 " 80 3,82 /j 57 5.IlS O.B45 0.21 O.~O 6,21 0,()4. (j Of) Mea.n u.bl)olutu devllJ.Lloll (1. 84) (1.1)0) (2 61) (2.48) 50.55 0.126 4.00 4 U3 4.94 4 84 4.85 o 225 5.00 5.HI 5 12 4.96 497 (1.377 [, 83 li.39 5.41 ILl 7 li HI 0,519 6 30 r..67 5.69 5 42 5.44 0.650 6. I a .i_ U5 5.97 5.70 5 72 O. Hal U 51 " 36 0.38 IllU 6.20 MlJlln ubsoJll.to dev.wtiuJ.l (4 8U) (4.15) (6, M4) (6 58) 101.0 0.277 5.94 6 2'l G 2fl 6,0·1 6.06 (l.aOI 6 01 6.28 6.30 6 07 Il.OO 0.451 GAl () 55 6.57 n.29 '6.31 0.018 6 75 6.87 I!. 8" 511 6.62 o 759 6.09 7.16 7.18 U2 (j,Un 0.769 7 01 7 18 7 20 b.96 6.9R Me~ll "boulut,e dllviatlOn (3.06) (3.34) (I 46) (1.31) 140.2 0.204 6.38 6.U7 U 68 0.50 6.02 0.505 6.99 7.24 7.20 Ii. 93 6.U7 0.694 7.39 7.63 7.65 7,34 7 38 0.768 7 51 7.79 7 81 7.54 7 57 Menn absolut,e dovitiotlOn (3.78) (4 02) (0.116) (0.85) 180.1 0,273 7.10 7.07 7117 7.35 7.35 0.365 7 _14 7.74 7.75 7.47 7.47 0.600 B.03 8.21 8.22 7.8U 7.80 0.714- S.10 8 45 R.46 8, III 8.10 Mean abEwlutlo ( levin.t,ion (5.39) (5.49) (2.65) (2.65) • experimental values are token (Pereira and Raw 1963) OaZculation oj thermal conductivieifl8 495 T.bI.3. Waoailjew& ooeftlcient. for ~ mixtUL't'S of N.-N.O &Dd ~-N.O mixtures Te"6erl\ture: From eq. (2) : From sq. (7) From uq. (3) : From oq. (8) 14)" All" AIj AI' A'/" AI'· AIj AI' N.-N.O 31.85 1.26 0.76 1.23 0.76 1.45 0.78 1.41 o 80 50.55 1.26 0.76 I 24 0.77 I 44 0.7& 1.42 0.79 101.0 l. 24 o 78 1. 20 080 1 42 079 1. 37 0.82 UO 2 1.23 0.78 1.19 0.80 1 40 0.80 1.36 0.82 IS0.1 1.22 0.80 1. 19 (I 81 1.40 0.80 1.36 0.82 O.-N.O 31.86 I :12 O.U I 28 0.76 1 49 0.77 1.45 o 79 50.55 1. 31 0.75 1.28 0.76 1 48 0.7S 1.45 0.79 101 () 1.29 1I 76 1. 25 0.78 1 45 o 79 lAO 0.81 1402 1 28 077 1.21i 0.78 I 44 0.80 1.40 0.81 180.1 1.27 0.77 I 24 0.79 1 42 0.80 1.30 082 'All v .. llles ...,e1.o.kOl1 from the referone. (Pereira amI Raw 11103) Equation (7) like Lindsay-Bromley method overestimates the Rystom N.-N.O genorally at all tivp tempera.tures by about 2·5 to 6'80/., and the systom O.-N.O by about 1·9 to 5'50/.,. Though for each system equation (7) shows more absolute devia.tions than the /cOlTespondmg Lindsa.y-Bromloy method, the compsrison is still sa.tisfactory. Equation (8) like M1Lson-Sa.xena method overestimates the system Nz-N.O by about 1·6 til 3·00/., at four tempera.turea but underestimates at 101·0·0 by 2·12°/0. The latter equation (8) overestimates the system O:-N.O a.t ]01"0 !md 180.1°0, but underestima.ws at other three temperatures. The modified form of Mason-Sa.xona. method shows better agreement with the experiment. 4_ CoDclusion Thora is a good agreement botweon the theoret.ioaJ and tho experimental values of thermal oonductivities of these bina.ry ga.s mixtures due to theso methods like the corresponding methods. It Beems that the approximation (equation (6)) taken is valId a.nd the equatIons (7) aond, (8) can be USl'd, frequently for binary gas mixtures. Ac:Jmowledgm.eDt One of authors (S.R.P.) thanks Dr. S. O. Gupta., Joint Director (Higher Education) U.P., Allahabad for inspiration and Dr. S. S. Kha.llna, Prinolpal of the College to provide the researoh faoilities to oarry out the resea.roh wOl'k at the Olollege. , 496 J D Pandey and S R Prajapati Reftlreacea Ch.apmQ,Jl S ami Cowlmg T G 1970 The Mathematica! Theory oj Non·un.Jorm Ga6cR, OamLridge U niver81ty PreBS, Oambridge Cowhng or G ID61 Prot. Roy. Boc. A. B88, IM6 C"wling l' U, GI'ay P o.nd Wright P G, 1963 PrOf. Roy. Soc. A .• B76. 69 Gl ... ~tone S 1974 7'hermorlyna~cB Jor OherniBl8, East·W'Bt Pw •• Neu, De/In HlrscllloJder J 0, Gurtiss C F Bnd Bird R B 1964 Molecular. 2'l!eor~ oj GaBes and LlIJuw., .1011,. Wiley lit 80f18. iflo. Lindsay A L and Bromley L A 1950 Illd Eng. Clleill., 42 1508 MlJ,bon E A and SILXBnB S C 1958 Phyg. Fluw. 1 361 POI'Olfll. A N H and Haw C J G 196:1 PhIiB. Flulrls 6, IOPI W .... dJewH A 1904 PI'1}B. 5. 737 Wright P G Bnd Gl'6y I' 1062 2'ranB. li'araday .'Ioc 58. I 

Calculation of Thermal Conductivities of Two Binary Gas Mixtures

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Calculation of Thermal Conductivities of Two Binary Gas Mixtures

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