Gambhir, R S

Saxena, S C

English

IACS Institutional Repository

Z E R O  PR ESSU R E JO U LE-T H O M SO N  CO EFFICIENT FOR  A  FEW  N O N -PO LAR G A SE S ON TH E M ORSE  PO TENTIALIt. S. (MMBHTR AiTD S. V. SAXENA jPnYaiOH DioPAiiTMENT, Kajasthan IInivishsity, JAirun, India (Jietxvjcd June 21, 1903)Keopiitly Konowalow, Taylor and Hirsclifoldc'r (I960, 19(il) Jiave iidded the Morse potential to the list of potentials lor which detailed computations of various f;as properties are possible This potential is (j>{r) — (.{x'^ —2 x),whereX  --- exj)[-(c/<T)(r-r„)].Here, 0(r) is the poti^ntial (uicrgy between two molecules at a separation distance r, 6 IS the depth ol the potential inininnnn at r — o' is tliat value of*/" for which=  0 , and c is a third parameter Avhich governs the curvature at the minimum and the steepness of the repulsive limb. Konowalow and Hirschfeldcr (1901) have determined the three parameters for a few non-polar gases from crystal and second vinal data. They also compared the experimental second virial values witli the calculated values according to this potential and the exp-G and Lennard-Joiies (12-6) potentials. This work revealed that most probably the Morse and exp-6  potentials are (jomjiarable in acciirac-y and both arc somewhat superior to the 1 2-6 potential. Saxona and Ganibhir (1963) have also investigated fhc second virial data of a few pure gases over a vdder tomjierature range, and also of a few gas mixtures. They Jbund the Morse potential to be somewhat superior to the otht)r two potentials. Saxena and Bahethi (1963) have calculated the trans­port properties in conjunction with the potential parameters given by Konowalow and Hirschfelder (1961) and compared the values with the experimental data. They found that the transport properties are not adequately reproduced and have expressed the necessity of redetermination of the parameters for an accurate relative assessment.T q  investigate the adequacy of this potential further we consider the experi­mental data of zero pressure Joule-Thomson coefficient, The theoretical com­puted values of the teduced //” are given by Konowalow, Taylor and Hirschfelder (I960). The experimental values of (C\ being the zero pressure specificheat of the gas at constant pressure) for He, Ar, CH4, and N2 have been reported by Lunbeck (1950). In addition to these values we also consider the experimental60540iJero Pressure Joule-Thom son Coefficient, etc. 541data of Budenholzer, Sage and Laeey lor CU4; and of Oharnley, Islow andTow i^Ujy (1953), UoeLuck and Osierherg (19 3 0 ) tdisak (1937), and OollhiH and (1939), (as reported by Cliaruley r^/ dJ 1953) foi’ N„ These experimoni-al values are shown plotted m Fig i Tlie eoniputed values lioth according to the Morse as Avell as the 7y- J  (12—9) potimtials are also shown. The exp-9 potential could not be consitlered lor the* theoiidical values ol tlie reduced are not available. We also do not consider here the J  (lS-9) potential introduced by Saxeiia and Joshi (1962) because though the rcdin-ed ji" is known, potential parameters for most of these gases liave not been deternnned as yet. The poten­tial parameters used in calculatTons are tliose tabnlatiMl by JvojioivaloM and Hirsch- felder (1991) except for Il(‘. It may be noted that lor botJi the jiotentials the parameters have been determined from the eipuJiln’ium pro]»eities only For lie we use the parameters of Bahethi and Saxena (1993) detmanined Irom the second vinal data, iiiese are . c - 4 ,  t//c  ^ 14.43'^K. and cr - 2 979 A.Fig. I - P lo ts o f iiH a function of tomporatnro Fo r Ar ordinates have beendisplaoed by -\-120 units, and for He abscissno and orrlinutos bavo Vjoori displaoed by -|~ 180 and + 4 2 0  units, lospeciively. Expenm ontal data - Ho, Ar, (4T i, N j, #  Lnnbeck; CH.j, O Biidonholzef et al.; N;), O Charnley ct a l , A GusaU, V Uoobuclc and Ormborg, Q  Collins and K eyes.From the figure Ave find that for Ar the Morse potential is better than the 12-G potential over the entire temperature range. For at high temperatures both the potentials are about equally good but the differences are ajipreciable at low temperatures. The deviations, however, are less for the 1 2 -0  potential. For both the potentials yield approximately similar results, ivith a slight preference542 R. S. Gamhhir and S. C. Saxenalor the 12  (i potential Home alternative (jhoices for the l2 -ti potential para­meters are also available for this gas Schamp Ei al. (1958) have reported the potential parameters for CVL^ ielk 148.07‘^ K. cr 3.810A) from the analysis ol their virial data. These parameters lead to values which are nearly 4% greatei than those plotted in the figure. Similar results are obtained it we consider tlu' potential parameters given by Hamann and Lambert (1954) lor CII4.Ill the case of He the 12 — 6 potential is definitely superior to the Morse poten­tial in tlie low temperature range even if the quantum eorreidions are (iOnsidered. Bahethi and Saxena (1963) have also noted that for He the above paramett^h’s completely fail to reproduce the transport properties They have determined Llie Morse potential parameters from viscosity data also The values aic' • c — d  e/A: =  S.55"'fv, and cr — 2.687A These parameters reproduce the tranBporl\ properties but fail m the case of second vinal coeffieieiit. If we use ilit'se para-\ meters to compute we get almost the same values al high teiupeiaf iirt'S butconsistently smaller values at low temperatures This disagreement will liirther increase if ejuantum c;orrections are applied.The above comparison leads to the conclusion that the L-~J (12-6) ])oteutial is slightly better than the Morse potential This conclusion is specially interesting in vicAv of the simplicity of the 12-6 potential. The fact that in thi^  case of He one set of Morse parameters cannot correlate both the equililirnnn and 11011- equililirnim properties implies that the Morse potential is not as good as the other two potentials, viz. 1 2 —6 and ex—6 , for this gasA C K  N O W  L  E  D G M E  N 'FWe are thankful to the (Council of Hcientific and Industrial Kesearch, New^  Delhi, for financial support. We are also grateful to Prof. J  0  Hirscbfeldcr for sending the reports in advance of their publicationsR E F E R E N C E SBahethi, O. P . and Saxena, S C., 1963, Phya. Flu ids inPrei>ti.Budenholzor, R . A ., Sage, B . H  and Lacey, W . N ,  1939, Jn d Eng. Ohem., 31, 3G9 Charnley, A , I hIoh, G L . and Townley. J .  R .,  1953, Proc, Itoy. Soc. (London), A 218, 133.ColhnH, S. G. and Keyea, F  G., 1939, J .  Phya Chem , 48, 5 Gnaak, I .  M., 1937, Phya, Z. Sowjet, 11, 60.H am ann, S. 7 .^ and Lam bert, J .  A ,  1954, Australian J .  Ohem , 7, 1.Konowalow, D. D ., Taylor, M H. and Hirschfelder, J .  O., 1960, Umvoraity of Wisconam Theoretical Chem istry R ep t. W IS-A F -16 .Konowalow, D . D ., Taylor, M. H  and Hirschfelder, J .  O., 1961. Phya. Fluids, 4, 622. Konowalow, D . D . and Hirschfelder, J .  0 . ,  1961, Pkys. Fluids, 4, 629 Lunbeck, R . J . ,  1950, D octoral Dissertion, Amsterdam R oebuck, J .  R . and Oatorberg, H ., 1935, Phys Rev., 48, 450.Saxoiiu, d  C. and B ahethi, O. P ., 1963, Mol. Phya. in Press.Saxona, S. C. and Gamhhir, R . S-, 1963, Molecular Physics, 6 , 577.Saxena, S. C and Jo sh i, K . M., 1962, Indian J .  Phys., 86, 422.Scham p, H  W ., J r . ,  Mason, E . A ., Richardson, A C B . and Altm an, A ., 1958, Phys. Fluids, 1, 329.

Zero Pressure Joule-Thomson Coefficient for a Few Non-Polar Gases on the Morse Potential

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/3789/1/Zero%20Pressure%20Joule-Thomson%20Coefficient%20for%20a%20Few_By%20Rs.%20Gambhir.pdf

Zero Pressure Joule-Thomson Coefficient for a Few Non-Polar Gases on the Morse Potential

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