Table Of ContentThe 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
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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
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Dxporimenfcal liethod and R e su lts................................................22
C alculations ...................................................................................... 25
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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
