Pandey, H C

Pandey, J D

IACS Institutional Repository

Effective Debye temperature and specific heat ratio in liquid methane and pentane.1 . D PaNJJKY AMD H C P a m d jc y  DeparlvieHi of Chevmlrff, of AIl(ikaha(f Allultabad 2110032[liemivfd (3 Mdjf 13375, rcvimi 11 Au<juA 13)75)As^ iuiDiuj^  quasi-ory»sttillmt  ^ Strucituvc oi li(|uulK, ("t1t\oiiYr l)cl>y(" tiijiijH'J'tiliu'us To]' tlio lifjuifis iiK t^liaiui and jimi-auf* aic. ojikiilatf'd as a luiuiiiuii oj' U‘nq)mitiin‘, anil prossuro i.tuujipratmcs lor liquid imuhaui' avo liinlu'r iisf'd m tioin-put.mg tli.o valuos of sjKUiiOo Kcaii I'at-io (y) aviUi i]i,o lu^ lp of oon.aiu jiai ainolei'  ^givi'u i]i .siaiidard Jitoraturo Tlic' A^ ahu's so obtaiiu*d aio lu Jan* agm’im'jit \v\x]i ihom^  puhlisliod oarJior TJu> A^ariatiou of 0 AAitJx tciiqxTatui o aud pn^ssiiu' is as usualNeutron scat-Uiriiig teolinupio (SmgAvi <d al lOOO, KgolstaK 13)05) and lulici’ t‘\i(U’ue(‘S (Hugluhs gI al 13)53), Hughes ei al 13)00) air aA^ aiJal)l(‘ in litriaturc* wJiirl; siipijorl the tiiiasi-crystalline luO;avionr ol luiinds Tlu‘ sinictnn* of Ji(piids can Ik^ (UuxoUhI by the term qiiasi-crystalluic in tht‘ sense fhal. tlii^ y display a ci‘i'tain degree; of local oi'diu* of the same typi* as lhal ol the correspcjiuling crystals. Tln^  study of dynamics oi atomic motion of liquids iilays vc^ ry nnporiaiit roll*, in undi'V standing lh(‘ solid like l)eli.avioiir of liquids ITufort iiuately no siicci'ssfiil tlu'ory IS .wailable in literature to exjilain sucli. dynamical bchavioiu’ ol' liquids On tli,e basis of quasi-crystalline inodiil, -JosIli (13301 ) and other (waliiated 1-lu' Debye bunjicrature oi Avaliu' at a pai’i/icular iempi‘ratiiL’(‘ aaIi.icIi, is in good agreement A\ it]i. tJu^  valuivs given by Siugwi el al (13300) Such type of calculations luwe recently iM'.eii ext(‘nded ( Koi’ gI al 1974, Kor gI al 13)73) to otlmi’ ii(|uids (uatiir, ethanol, imulxauol toluene, hexane) assuming llie aiomic motions in tlu'Si' liquids as similar U) ’ I lose of solidsIn all the above mentioned mctliods of lialciiUting tlu‘ values of Debye temperatLU 'o, tlie ultrasonic absorption and sliear viscosity data w c j (‘ employed. Th(‘ prciseut paper deals with tJie evaluation of (dfcctive Debyi  ^ t(‘mp(*ratuve ol liquid pentane and liquid nictham^ as a lunction ol tinnjjeiaturii and pressure assuming tJi.e q^la^si-crystalline model for these* liquids Hei'c a vc  Ju ia u * modified tin* usual procedure for calculating the Debye teinpci atiire so as to avoid llu*^  usii ol ultrasonic absorption data.The previous workers calculated tlic valints of 0 (Kor at al 1974, Kor al al P-173, Joshi 1961) by using the pannm'tcr A giv(*at beloA\hiihun ./. Physia. 49. 8«9-872 (1!)75)( I f f ) ( : ; : )  ( i ) ’(1)86910870 j . D. tandey and H. C. Pandeyrrwhoro all iho teumfiJ have their uKual aignificaiico, further tli,o ratio r an In*smix)]ifiod hy uhjjng the v^oll known roJation1^T,o1_K tjOJAnd simplified relation can written as,/ ^T,co \ / \\ KTn / ~  \ K t .o ) 1 - 1 -1 - r(^ )Ci)Mherc^  y  is the heat capaeitic'S ratioAc(5ording to Litoviiz ik Davis (1965)7 n OWe have from eqs (2) and {4)i]vI n - /  3 \ i]v I —Avhich reduces toCombining eqs (6), (3) and (1), we get A1 - y+  yi^ y)(7)J^ Vom this roJaiion, the Poisson’s ratio is givem by (Joslxi 1961)_ («)Thus we nc(id only y, p and /Jt ,cc for cajiailaring the effective Dehyi* uiii- p eratu rci 0Resulls and D'U'C‘m.nonData on ultrasonic moas'iirements in liquid methane (Sing^ r^ 1969) and liquid pentane (Ric]\a"‘dson 1957) Jxave been utiJisod for calculating the values of 0 al different temperatures and pressunis “Tn case of liquid methane, the valines el 0 were calculattxl at. constant pressure with variable temper at lU 'e , at constajii tcmi>erature witJi, variable*, pntssuri^ and at cimstant density with variable tcin perature  ^ and prossurii A ^ 'J l J le  m liquid fientajK^ only p r e s s u r l ^  is varied. F u J i U e i ’, 0 values for liquid methane are utilised in computing y values with the help oJEffective Debye iempcratvresiaudard literature (American Institute, of riiysic.s Handhoi.k 1 ftc,:!) 'Pii,., ijl’ above calculation are presented in tables l and 2Table 1 Temperature dependance .,f Del,e;„. I.nuperature (I for liquid methane at const,ajit iirc'ssure I (i8 kfj/cni-S71T o m p o it i t i ir e  m  "KD o n s ity  m  g in /c 'c .0in  'K: rm1 1 2 0 ,4 2 1 94 15 1 S5 1 7(i1 0 5 0 4:iR I d s  9S 1 S3 1 729 4 0 4 5 0 n o  18 1 84 1 09'•‘iSiripor T  R .  I 9 6 0  .7, C h n n .  P h y s .  5 1 , 4 7 2 9Pj’os.^ iirc^  dopojidonoo of D(d)y(^  tonij)oJ'atim at coriHiant temperattiro (112 0‘ 0  foj ]i(:L- ] ) ' K|uid mctli,an(^P ro ssu rp  ill k g/cn i®D e n s i t y  ill K m /r (’0111 'Kycrrl y'^uf1 OR 0 4 2 1 94  15 1.811 1 .7 0:i(» R 0 4 2 4 9S 0(1 1 RS 1 75(1 2 .5 0 4 2 7 iO l 50 1 s.n 1 738 9  0 0 . 4 3 0 104  90 1 83 1 74J .  11. 1 0 6 9  J . Chpm. P h y n  5 1 . 4 7 2 9qVmp(^raturc and prc'.ssnro dopon<lanc(‘ of T)ebyi‘ tomperatiirti for liquid methauo at constant density 0 420 gm/c cProflsiiive in  kjT/cinn®T o n ip e r a tu i'p  in  ’^K0in  “Kyf'rO2 4 1 1 3  0 0 1 .8 0 1 90 1 787 . 9 1 1 3  (J 01 SO ] 80 1 ,7 01 4 .1 1 1 1 ,0 01 8(^ 1 .8 0 l .S O2 7 . 0 1 1 5  0 91 80 J 89 1 .8 15 2 . 0 117  0 93 77 1 88 1 .8 3♦ S in ^ n r J .  R .  1 9 0 9  J . Cham. 5 1 , 4 7 2 0 .A,s flocn from table,s, Dobyo t.HTnpt'raluri* 0 incJ'oasCiS with proMiS'iiro for botli liquids while decreases with temperaUirr for liquid TUethano. I t its iriiereflting toTable 2. Pres,sure (lopentVmee of 0 for liquid pontano at 15*^ 0872 J. D. Pandey and H. C. PandeyProasiire in kg/cin“0in "K00 0 33.2707.0 34.3314.1 35.7821. J 36.162S.1 36.3935 2 38.49A2 2 39 4049.2 40 1756 2 42 . IKnote t]i,ai />did not eliange at consiani d(^asity wluJe l^inp(‘ratur(‘* and jiros.smv were', varied. The variation of and its magnitudes for beWh ili,e liquids an^  A/ejy similar to thOiSe of non-assoenated liquids (Kor of al 1074) wnich vas expeeie’d a 1st) y values for liquid whicli, were' deTive l^ frenn ea>m‘Spondiug Desbye temporaluirs on assumption that liepiid liebave'.s as seilid, ai'e ve'ry close*, to those* (Singe*]' lO(iO) publisluid previously ami luuice* support tlie* quasi e*rystalliue^  imieleJ lor lie|Uiels "Due te) lack of Op value's, no coinjiarisiou ceuild be maele* for liepiid pemiane* More'- e)ver. sinnlantie*s rogareling the magnnuele. anel nature e>f variation ei f lei r  liepiul pentaim with iion-asseieiateHl liquids are. suffieiicmi basis for tlie jirtMlieitiein e)l n.s values Tims the results se> obtanmd can be snmmai'ise r^l by stating thai the Pehye* temperature* in liquids may have more or less the same moaning as in soliels foi' the iiiteraetioii oF the* order of sec.Authors are thankful te> >S C.S.T R. (U P ) for preividing the financial assisiamoReferencesA m e n c a i i  I n s t i t n t o  o f  V hvsicH  H tirid  B o o k  (JSIe’G r a w  H il l ,  N o w  Y o r k , 190'J).K iiK ol-fetaff P  A 1 !)65 T h e r m a l  Nc,iHro}i iScaUf^/nig. A ra c lo m io  l ‘r(iSH N o w  Y o ik  H u gh oB  I) d . .  P o le*vsk y  H . ,  K le y  W  'T iin b o lo  E  P h y a ,  JIpv L e f ten t  3 , ^ 1  H u gh oB  D . J , P a le v a k y  11 ,, K ie v  W  & T u n b lo n  E  I9G0 Phy>^. Hev.  1 1 9 . 8 7 2 .Joshi S. K 1961 J  OhEw Phya. 35, H HKor S K , Prasad R & Agrawal A 1973 Acuahva 29, 240.Kor S K. & Tripath] N O. 1974 J Phys Soa-Japan 36, 552. liiiovil7 T A & Davis C. M. 1965 Physical Acoaatich, Vol Ha.Riohardon E. CJ. 1957 The International Union of Pure and Applied Chemiatry, Tho Instil nk' of A'le^ chanioal Enginoors, iSo9.Bionl, ptipoi 6 Singer J. R. 1969 J ’ Chem. Phys. 51, 4729 Singwi K, S. & Sjolander A. 1960 Phya. Rev. 119, 803,

Effective Debye Temperature and Specific Heat Ratio in Liquid Methane and Pentane

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/6229/1/Effective%20debye%20temperature_J%20D%20Pandey.pdf

Effective Debye Temperature and Specific Heat Ratio in Liquid Methane and Pentane

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