The Pennsylvania state College The Graduate School Department of Physics SUPER SOW IG iiSASUHEMChTS IK CARBON DIOXIDE, HELIUm, AND CARBON TE TR A FLU OR IDE h alter Hayden Byers A d isse rta tio n submitted in p a rtia l fu lfillm ent of the requirem ents for the degree of Doctor of Philosophy at The Pennsylvania State College State College, Pennsylvania December, 1942 Apor o ve a ; De c emb er/^ 1942 Department of Physics Dec emb er 9 194-2 14______________ Head of the Department /vS.-.— 0 S.L'j_ lu i: l! ;_J iho aathor wishes to tshe this oppor­ tunity . to tho.nl: a ll who have directed and assisted him in this work. He especially wishes to express his apprecic tion to Hr. h. H. Pieloneier for his continual and tin- Tan cl in s: Guidance. c i ■J .L a jl. .JL Page pari I - ua^!JRRira:ar III ojaaor ^ io r iia .................................................1 I n t r o c u c t i o n .......................................................................... i 'fcroor iraent s.1 Ho thou................. ............................................................ 2 Ih o o re tic sl C alculations................................................................... 4 R esalts.............................................................................................................. 8 D iscussion oi R esu lts.................................... 13 ?AT.T II - IRlUinRRIRRII II: HI3LIUI.I........................................................1 9 iT.) •. * 7UA. .r1 Jt- tX "" -:i ■ rp ' ■r-•! r . : > ' p• - • X •-> XTr-*. nR il-.'.V - /wv'-l.r -- Li-tU-< -L, r.p . 4'•i - ;it T'TJ/XPl ^TR”'* ".-i* • • • • « • » « • n Dxporimenfcal liethod and R e su lts................................................22 C alculations ...................................................................................... 25 % , ,. . 7r>r t rv.T”' n /. Td — r it r*iprh? l xiT jrr'* T ^ PR 4^.4. ,j ^ Xa'i. I V .. ...a.J RXi- • - X - . - .ii -A ‘. X./. . X—' .4 • • • » * • « • • • • BIRIIC-RARMI................................. 29 i PART I MEASUREMENTS IN' CARBON DIOXIDE 1 INTRODUCTION measurement of the absorption or supersonic waves in carbon dioxide with added water vapor at 301°K reported by jrieleuieier, Saxton, and Telfair ^ seem to indicate, by a secondary hump on ohe aosorption curve at a. relatively higb*- perceiibage of we ter vapor, that for these conditions energy' in the longitudinal (or valence) mode of vibration of the carbon dioxide molecule may have a different relaxation than the energy of the transverse (or deformation), mode o f viDi&tion. However, their resu lts were not conclusive for several reasons. 1 ) a theoretical curve plotted on the basis of two different relaxation times yielded a much smaller secondary peak than that observed. ?>) Leonard had to assume equal relaxation times in dry carbon dioxide in oruer to account theoretically for the height of the p e s ^ * 3) On the other hand, a curve by Fricke ^ ^ for absorption in dry carbon dioxide might be interpreted to show a double peak if he had not so completely smoothed, out the curve through the scattered points. The earlier work with 0 0 3 at 301 K indicated nearly eaual life times for low HpO co n cen_ tra t io n s. wecguse an increase in temoerature will increase d isp f portionuuely the contribution of the valence mode of vibrab i ° n to the internal energy of the molecule, it was decided to f e ~ peot the measurements of Fielem eier, Saxton, and Telfair &b a higher temperature (371°K). 2 EXPERIMENTAL METHOD The apparatus used is that described by Telfair and Pielemeier with a minor addition to more accurately deter­ mine the water va.por content of the carbon dioxide- The carbon dioxide was obtained from dry ice and passed through a humidifier consisting of two lin es in p a ra lle l. One line contained P3O5 drying tubes; while the other contained bub­ blers immersed in a thermostated water bath. Thus water vapor contents below the vapor pressure of water at 0°C- could be easily obtained by regulating the rate of flow in the two p arallel lin es. The carbon dioxide entered the supersonic . chamber near the bottom and flowed out through a tube near the top. The emergent gas then passed through a General E lectric Dew-Point Potentiometer in order to measure the we ter vapor pressure. This was then reduced to the mole per cent water in the m ixture. In th is way the gas was flowing quite slowly but steadily while the supersonic measurements were made. In order to allow the walls of the chamber to reach equilibrium with the water- content of the gas, the gas was allowed to flow for some time un til the Dew-Point Potentio­ meter indicated that the emergent gas had a constant humidity. (Before c-he gas was admitted to the chamber at a ll, it was, of course, evacuated.) The dew-point of the carbon dioxide was checked several times during each run and was always found to be constant to within a degree or two Fahrenheit. The order in which the data were taken might affect the resu lts if a system atic equilibrium lag occurred between the 3 water in the gas and. that adsorbed, on the chamber w alls. The 442.8 kc and the 549.8 kc data were taken almost at random hum idities; while the 614.6 kc data were taken startin g at 2.98 per cent water vapor and running to dry carbon dioxide, then beginning at 3.14 per cent and running uo to 4.02 per cent. The two sections of the plotted re su lts joined nicely. Thus, any effect of the adsorption of water on the walls is thought to be absent. Tempera.tuxe was measured on two cooper-constant an thermo­ couples carefully calibrated against a standardized couple of the Petroleum Refining Laboratory of th is college. They were located at different levels in the gas chamber, and the heat from an auxiliary heating element in the surrounding oven was adjusted to make the couples read like temperatures. Thus in- the small distance used, there was only a negligible temperature gradient possible. A hollow cylinder of cooper lined the supersonic chamber to help equalise the temperature. The absorption coefficien t oer wave length J^ ) was ob­ tained from the logarithm ic decrement of the variation in plate current. This was done by p lo ttin g lognl^vs resonance peak number. The curve resu ltin g was always a straight l in e . Then the absorption co efficien t was obtained from the equation = 4.606 x slope. The fact th at s. straig h t line occurred, together with the fact tna.t the conditions developed by Hardy* for the v alid ity of H. C. Hardy, Doctorate D issertation, The Pennsylvania Stai,e College (1941). 4 the above equation were fu lfille d , gave confidence in this method of calculation of absorption co efficien ts. For this purpose, and for that of getting wave lengths, it was usually impossible to use more than 15 to 20 resonance positions of the reflecto r because of the great absorption in carbon diox­ ide and the necessity of fu lfillin g the conditions already mentioned. However, the re su lts of these 15 to 20 positions were so self-co n sisten t that l i t t l e uncertainty remained in the value of the absorption co efficien t or of the velocity being determined. THEORETICAL CALCULATIONS The internal specific heat due to the vibration of the carbon dioxide molecule was calculated from the frequencies of vibration given by Sooner (1?) equations given by Fielemeier-, Saxton, and Telfair (1). I t was necessary to use up to the 4th quantum state of the deformation mode, to the 2nd state of the symmetrical valence mode, and only the 1 st state of the unsymmetrical valence mode of vibration. Trie resu lts follow; Mode Ci (370.1°K) 03,(371.0) 0 . 300 0 • 302 ■*£ /) 0.016 0.016 Total 2.547 2.55o Cal/mole 5 Considerable d iffic u lty was encountered in obtaining reliable constants to use in theoretical calculations of the absorption co efficien ts, and in calculation of velocities in dry carbon dioxide of supersonic waves of the frequencies and at the temperature used- Prim arily, i t is necessary to know the ordinary, equilibrium state, value of the specific heat at constant volute (CQ). The reported, values of th is constant and of data from which it may be calculated are quite conflicting. Values of C have been found in the lite ra tu re ranging from 9.11 cel/mole to 9.70 cal/mole If it is desired, to calculate the specific heat from velocity of sound measurements, it is necessary to be sure that the fu ll specific heat is still, effective; that is , that a sufficiently low frequency has been used. To be sure of this, the location of the velocity dispersion region (obtain­ able from a value of the relaxation time) must be known. Here again contradictions were encountered- linen Richards and , . (5 ) ueici's measured velocities of y kc sound in pure carbon dioxide are extrapolated beyond their 90°0 value to 100°C, either by the method of lea st squares or graphically, a. resu lt of 398.0 meters per second, is obtained. They believed that Dispersion had already begun; yet King and. Partington ( ^ give 300.1 meters per second as the velocity of 3 kc sound at 100°C. However, Eucken end Becker ^ ~ ^at 75°C end 58.4 kc give a velocity of 397-5 meters oer second, while a. graphical • 4- (6 ) interpolation of Van Itterbeek end n.eriens' data at 598-99 kc gives at 75°C a velocity of 303.2 meters oer second- These 6 last two values together with Richards and R eid's 9 kc value of 239m eters./second at 75°C, would locate thed isoersion region in then eighborhood of 40 to 50 kc; a fact which is not supoorted by the relaxation times given by either van Itte r- beek and imriens in the same a rtic le , or by Eucken1 s coworker (1 a ) kuchler v kucnler gives the following data for the relaxation t imes: t°0 19 100 /3 xlO6 6.0 4.8 rat-* while Itterpeek and mar lens give (when extraool&ted from 80°0) t°C 19 100 ^ ^ x l O 6 1 1 .6 8 .0 * (*The value at 100°C is very uncertain but th is is the lowest that the data w ill perm it.) If there is but a single disper­ sion region in dry carbon dioxide,-- the inflection point would then be located as shown: by Kuchler at 26 kc. (100°) by Itterbeek at 15 kc. (100°) The inflection noints at room temperature would agree qual­ itativ ely with Richards and R eid's findings of too large a, value of V0 when 9 kc sound is used. The resu lt of a ll th is confusion is that no completely independent th eo retical check on the resu lts of the experiments herein reported could be obtained. So the author resorted to the following process: In view of the low frequency of the inflection point of rhe disoersion curve, it was felt that at the frequencies used the vibrational specific heat was comolete ly inactive in dry carbon dioxide. Therefore, the average of