Saksena, M P

Saxena, S C

Saxena, V K

English

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6SMEASUREMENT OF THERMAL CONDUCTIVITY OF GASES USING THERMAL DIFFUSION COLUMN : NEONV. K . SAXENA, M. P. SAK8ENA and 8. C. SAXENAPjJYaios Dei'ar.tmtont, Pajasthafj Vis'iVKiiajTY, tlAiPiJJi, India [Rvaaved A^jril 14, lllOO; Rt\'^ ul>initlcd Juvc 4, l!MUi)ABSTRACT. A Jitili-wiro typo ol tlioiiruil tliffiihiuu nilninn jn cil In inonMirntliomi'il o )aiiuctivity of gUKos. ]\1ortMuromoiith on l ouji nrn in]j(rUul m Mm urn mn^ mliU.J-7:i.'3‘^ lC iiu d  lo i tivH ( lilfn io n t vahioH id prnsMitv sjohUoi' Mwin aji aUao.spljiMi' 'I’lm \ailm.' ugroo axn:)Jigst tliemsolvos wiMim h hoaitni id nbnut r> pni coTit tmd atill botlnr y'iMi Min nllim nxisling liUmitui'R v/iliio-i obtiMnOLl IV.im odynlilKshnfl nnnvn itiniml todniKiucs Tim Mini'nf-'{ obtfiiuod iH parbionlarly gratifying wdion tlio iimafinnl, of Mmraitil cimdimtivjb^  iiinKMirniimnMi at higher toinjJoratui'os rooaJled] N T I I  0  D  IJ C T I  0  NMcasuroments on thermal conductivity oi gases and ]jarticularly at Idgli temperatures are of gt‘cat importance to sciontiatH as well as engiiK'ers. ]<or l-hc proper understanding ol the exchange of eiicrgj'^  between exlenuil and intei'na) degrees of freedom of polyatomic molecules such an information is basic. A variety of design engineers also very frequently and in an important way lUH^d such values,Tt has long been known that reliable and accurate measuMunent of thermal comluetivity of gases is probably the most diffi(!ult amongst all the transjiort properties. This is because many complicated corrections arc to lie consjdered and the job becomes increasingly difficult as the teinjicraturo of imnisiiieinent, is increased. Purely on the grounds of need in the recent years several very impi(i.s- sivc efforts have been made for measuring thermal conductivity at higdi tempera­tures. Here wc report a part of our oontinuing effort to cleiermmc thermal conductivity using thermal diffusion columns.The use o f columns for thermal conductivity measurements was first suRgested and employed by Blais and Mann (1960), who reported results on helium and hydrogen in the temperature range 1200-2000°K. Th,i accuracy of these data is doubtful and it is believed that then values are systematically greater than the actual values, Saxena and Agrawal (1961). A few more arguments m tavoiu of this possibility havo been advanced by Saksena (1965). In this laboratory we have revived this work and very encouraging prehminary measurements h a ^  reported on helium and air, Saksena (1965). He employed a s y s t o  of two glass eoLmns completely identical except for length and measured the thermal eondue- tivity in t h e ^ p e L u r e  range 313-413”K. Differential measurements were taken597 ■5 98 F. K* Saxenay M, P, Saksena and S. G, Saxenato avoid tho probable losses due to end conduotion and these were also theoretically calculated and found to be always less than 0.6 per cent for air and still smaller for helium. These measurements conclusively established tho teclmique in this temperature rangt^  because these values wore found to be in good agreement with the directly measured values by tho conventional thick wire variant of the hot­wire cell, Gambhir (1965) Encouraged by the success of the results obtained wo have launched a full range programme to measure thermal conductivity of various pure gaacis as a function of temperature. This effort has to be preceded by carefully planned sots of crucial runs which may unambiguously citablish the technique and provide a clear idea about the precision of measurements In tho present article we report the measurements on neon in the temperature’^ range 323-723''K at five different pressui’es and compare with the existing data obtained from conventional techniques.T H E O R YWo now present a brief and relevant account of the theory of this method as particularly applicable to our apparatus design. Assuming tho wire to be at a uniform temperature, its ends to be at the same temperature as the cold wall, convection to be absent and the heat flow to be radial, we can write tho differential equation giving the heat flow as ;naHC -2nah,0-Q r-^ Ppo{l-\-aO) =^(). ( 1)Here K  stands for the thermal conductivity of tho material of the hot wire of radius a at a temperature 0 above the cold wall temperature*.. The wire material has a temperature coefficient of resistance a and pQ is its resistance per unit lengtli at 0 =  0. I  represents tho current through the hot wire and J  the mechanical equivalent of heat stands for the loss of heat from the wire per unit area per unit temperature difference by conduction through the gas. Similarly Qf repre­sents the quantity of heat radiated from a unit length of the wire.If the column is highly evacuated so that \  =  o, eq. (1) reduces tona^K =  0.dz^  J ... (2)Hero r  represents that value of the current which maintains a particular element of the hot wire to be at the same temperature in vacuum as a current I  flowing through it does in the presence of the gas.Subtracting eq. (2) from (1) we get for the power conducted through the gas(8)Now two more reasonable assumptions get assooiatcd with equation (3), These are . (a) The temperature distribution along the length of the wire remains praoti- caUy unchanged with or without the gas, (b) the heat lost by radiation is inde­pendent of the nature of surroundings. For a sufficiently long wire the lengths at the two ends where the temperature may be appreciably different from Ibe uni­form temperature in the mid region will be relatively small and the first assump­tion will be reasonable The second assumption is also valid as under normal operating conditions the gas in the column is invarialily transparent to thermal radiations. We therefore get for cyliiidi-ical geometry and radial heat How conditions27TahJ3 =  — 27raA(—^  )Meaauremmt of Thermal Oonductivity of Gases, etc. 59927tA  ^Injbja) . . .  ( 4 )Here A is the thermal conductivity of tlio gas at th(> wire tcmjicraturo and 6 is the radius of the cold wall. We have consequently,27tA fi ln{b/a)The eq. (5) leads to/ dcOo \ __\ W  )r=a~2nXln(6/a)’( C )and alternatively. _  h^ja) { dfa)c\27t"  I dO Jr(7)E X P J i K I ME J MT A LThe principal component of our experimental assembly consisted of a con­ventional hot wire type thermal diffusion column. In princiiilc it consists of a precision bore tubing, along the axis of which is run a uniform platinum v^irc. Through suitably designed arrangements the electrical connections to this wire are brought out. A great care is taken to ensure minimisation and constancy of contact and stray resistances and in oui* arrangement their magnitude never ox ceeded 0.02 ohms. The outer wall is maintained at a constant temperature by circulating thermostatically controUed water in the surrounding jacket. The relevant constants of the column are given in Table I. The wire is maintained at different temperatures by passing appropriate currents through an arrangement2which is energised by a number of high capacity lead accumulators, The column can be evacuated to high vacuum (10”® cm of mercury) by means of a metal pump­ing plant comprising of a two stage rotary and a high capacity oil diffusion pump etc. The potential across the wire and current through it are measured by a sensitive Tinsley vernier potentiometer tyj)e 4363D and other accessories. The constants A and B  of the platinum wire occurring in the relation6 0 0  p', £ .  Baxma, M. P . Saksena and S. G. BaxeM(8)are determined by a separate set of exporimonis. These are also required jn the calculation of A and are reproduced in table T. The detailed description is given by Saksena (1965). \TABLE 1Geometrical and electrical constants of the conductivity columnLoiigth of the platinum wire ... 91.56 cmRadiuH of the wne (a) . . , 0  024G3 can,I i i to m a l diam etov of tlu3 colum n tube (2b) 0.8544 cm.E x te rn a l d iam eter of the colum n tube (2b ') .. 1.023 cm.flenatarioo  jie r u n it  leng th  o f th e  p la t in u m  w iio  a t0°C (Zfo) 0.0054477 ohm/cm,The  ennwtant A  o f the p la tin u m  w ire  ... .. 38.25 XThe  conytant B  o f the xAatiiium  WJVe . . ... — 4 9 x  lO 'S /^C^In nut-shell the procedure amounts to measuring the power required to heat the wire at any arbitrarily chosen temperature with and without tho test gas. To achieve this in practice measurements are taken, in vacuum and then with gas, of the resistance of tho axial wire when a known current is passed through it. In Table II, wo report the computed power at our directly observed points as a functions of temperature for vacuum and for five different pressures. The tem­perature of the hot wire in each case is identified by its resistance and assuming this variation to be in accordance with relation (8).^To compute A for each prossiiro separately, W  and Wr arc plotted on a largo graph pax>er versus temperature and by point to point subtraction a third curve IS generated on the same plot for as a function of temperature. Here W,Wf and Wc are the powers fed to tho wire, with tho gas, without the gas and conducted radially through the gas respectively. Next Stirling’s formula is em­ployed and the quantity oomputed for equally spaced values ofIfMeasurement o f Thermal Conductivity of Oases, etc. 601>.a.5 I§o ^^ ^ c\PJ4<DI IO) .o>S !■S “(-1I‘SrtJIiS1(51(3fO■HHCCeclOCDl -CDC3oo  oc-i i - Jz; CO 00l l3O <M ec CO C3 D1 oi05IM lO eo L ' ~ CO oiO'C5C<3nccBOcDctocO5  SI'- oi00lO1^1ost -Oo0505o(MMo omCD C-o C-I r i IDo (M - f CD QO M -CCC4O'CCCi oictriCDQO co O to 00 >D COCD CD(M OCOCO05cOi " 01CCCD<No(MCOeftCC05lOntQOOsOCDiDCOin•005o05oi 'CDoCD05IDCD(T»CDCDCD> o o o oeo. st'- ffs -It CO CO05 05 ClIMCDCSO1'03o05eo ao MIM§oeovt(CO602 V. K. Smena, M, P. Saksena and 8. C. 8axenaTABLE IIIValues of 10®X in cal cm~  ^ sec deg~  ^ for Neon, at different pressures, p, in cm of Hg as a function of temperature inTom p. p  =  10.2 p  -= 17 5 p  - -  29.3 p *  ^  47.4 P  — 60.650 1 2 .3 12 1 1 2 .7 1 3 .6 1 2 .6100 13 3 14 0 1 3 .0 1 4 .9 13 7160 16 0 14 4 1 4 .7 16 9 14 7200 1 6 .7 16 4 1 6 .8 1 7 .2 16.1260 1 6 .9 1 6 .0 1 7 .4 1 7 .7 1 7 .9  1300 1 8 .1 18 1 18 4 18 2 '360 IS  8 19 .3 19 3 1 8 .7  \400 20 .1 20 .1 19 3450 20 5 19 6*  T liis  .set is som ew hat uncortain  due tn  the  in .stab ility  o f the  e lectrical c ircuit.The calculation of A is now straightforward on the basis of relation (7). These values of A are recorded in Table III and are shown plotted in Fig (1). It is rele­vant to point out hero that while taking measurements at 47.4 cm of mercury the electrical circuit was somewhat unstable. This, we feel, might have caused uncertainty in the readings of unknown magnitude. We therefore in interpre­tation of our results do not give any weight to this set of data. Nfevertheless, wo have shown them plotted even in Fig. (1). It is interesting to note that the obser-i . j. .-.j, A /s ■ vr- uiu. ■‘aou vuL'Hua \j), Each Hot of points refer to !iparticular value of the proaaure (in cm. of mercury). Thus, O, 0 ,  0 .Q  and • refer to 10 2, 17.6, 20.3, 47.4 and 60.5 rospeotivoly. The continuous curve is obtained as a best oompromiso plot of all the other existing X values,TOtions even at a pressure higher than this value viz., (iO.5 cm of meroury arc in accord with the throe seta of diffci-eut observations alt at smaller pressiin's, We hasten to state that all the four sets of A values show no systemalio difference of any particular typo relative to each other as a function'of toinpcnviurc. The directly calculated A values show a .scatter of about 5 per cent and a(. various tern- peratures it is even smaller. Let us now discuss the, important corrections to be applied to these computed A values.The coiToctions likely to bo of importance for measurcmoiitH by Lliis method are : (a) convection, (b) temperature jump, (c) wall aud (d) end olTcctis. To dis- cover whether the first two effects are involved in a partienlar meaHurrment of this type there is an entirely experimental procedure possible 'Phis has boon well known to experimentalists of this field and consists in taking ineasim'nKMits as a function of pressure. It was for this reason that we look measurements m tlie range 10.2 to 60.5 cm of merciiry and for five different, value,s of pressure. While taking the measiiromonts it was also Impt in mind to det oet if there is any syste­matic variation, howsoever small, with the change in pressure, In the previous measurements pressure dependenee was observed only around 2 cm of mercury, Saksena (1965). We thus conclude that for our ajiparatus and these operating conditions both convection and temperature jumy) olT(‘ets me negligible. The calculation of wall effect is fairly well knoAvn and is described in detail liy Saksena (1965). This effect which arises because of the finite conductivity ol the material of the cold wall was found to bo fairly small for our mcaHiiremoiits, To quote for a numerical estimate it is only 0.3 percent at 50°C and rise,s slowly with torapera- turo assuming a maximum value of 0.5 percent at 450®CThe last correction i.e. the end effect is probably the most imyiortant of all and unfortunately is least understood. Tliis obviously appears because of the conduction of heat through the two ends of the hot wire and causes a nonuniform temperature distribution along the wire. As it is not simple to rigorously account for this shortcoming a brief discussion regarding its probable consequences will bo in order. It may be stated that for a sufficiently long and thin wire this complication is likely to be small and we took the full advantage of this fact and kept the uncertainty on this score to the minimum The calculations of Saksena (1965) based on the theory of Gregory and Archer (1926) yielded that at 100“C for air the correction is about 0.6 percent and further as the conductivity increases the magnitude of this correction decreases. Thus, for neon it will ho still smaller. However, it is not possible to apply this theory as the temperature further iu- croasos. Saksena (1965) has further tried to eliminate tliis olfect by taking dif­ferential measurements on two columns identical in all respects except length and connected in series. It is believed that under such conditions the measurements taken refer to a small central region of the longer wire at a umform temperature. His work with helium revealed that till lOO'^ C the effect of end conduction on theMeasurement of Thermal Conductivity of Oases, etc. 6036 04 V. K. 8axena, M . P . Saksena and S. O . 8axenafinally calculated A values is negligible We propose to consider both these points in our work at still higher temperatures than covered in the present effort. The situation which prompted us to adopt this approach consisted in a comparison of our measured A values with those existing in the literature from conventional and accepted techniques. Gandhi (1966) has recently pooled together all the available data on rare gases as a function of temperature and recommended a .set of best compromised smooth values In the figure we show these values by a continuous curve, it may bo important to mention that there arc considerable scatters in the data at different temperatures and a serious guidance is drawn from the measurements taken in this laboratory by a hot-wire coll, Gandhi (I'pGG). Tt is particularly gratifying to note that the smooth curve posses well tlirougli our observed points lending thereby a very good support and reliance in our present measured values. Wo hope to further extend this work and bring to light the intricacies, if any, by suitably XDlanned programme of work Thus, this work as well as earlier, Saksoua and Saxena (1966), tend to establish this technique and its successful performance only upto the maximum temperature of 713°K. On the basis of this promise we are extending the scope of these measurements to still higher temperatures and will therein take into account all those corrections which may then become appreciable and are negligible in this temperature rarige. Our present experience based on the work in progress and going upto 1300“K indicate that this technique is capable of yielding sufficiently accurate and reliable values.A C K N O W L E D G M E N TWe are thankful to the Department of Atomic Energy, Bombay, and Council of Scientific and Industrial Bcscarch, New Delhi, for financial support. One of us (V.K.S.) also acknowledges the award of a research fellowshipU E F E K E N C E SIhtUH, N. C. and Mann, J. ]3., 15)00, J. Oliem Phys , 82, 1459.Gainbbir, R S , 1965, P h .D . Thesis, Rajasthan Univoraity, Jaipur, India (uripublishod), Gandhi, J. M , 1960, P h D .  Thesis, Rajasthan Universily, Jaipur. India (unpublished) Gregory, H. and Archer, 0. T., 1926, Proe. Hoy. Soo. {London), A, 110, 91.Stksona, M. P., 1965, Ph.D. Thesis, Rajasthan Univer.sity, Jaipur, India (unpublished). iSaksena, M. P. and Saxena, S. C., 1966, Defenoe Science Journnl {in press),------ --------------------------------------------------------- 1966, Phys Fluids, 9, 1695Saxenu, S. C. and Agrawnl, J. P,, 1961, J. Chem Phys., 84, 2107.

Measurement of Thermal Conductivity of Gases Using Thermal Diffusion Column : Neon

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Measurement of Thermal Conductivity of Gases Using Thermal Diffusion Column : Neon

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