Measurements of the thermal diffusion factor in the pressure range 1–400 torr.

Van Dael, W. Van Itterbeek, A. Cauwenbergh, H. 1966

Physica 32 621-624

LETTER TO THE EDITOR Measurements

of the thermal diffusion factor in the

pressure range 1 - 400 torr. Already many years ago the pressure dependence of the thermal diffusion factor has been investigated at very low pressures by Bet key and Grot h 1) and at high pressures by Becker 2). More recent investigations in general confirm these original results, which can be, at least qualitatively, quite well interpreted. In 1962 K o t o u s o v 3) carried out measurements in the intermediate pressure range. He observed a slight decrease in the thermal diffusion factor OL of several mixtures for pressures between 1 and 0.25 atm and a very sharp fall-off below 0.2 atm. Neal 4) drew attention to the fact that discrepancies exist between theoretical predictions of the L J potential model for the variation of OL with temperature, and some experimental data in the neighbourhood of the inversion temperature. These experiments are all carried out at relatively low pressure and the observed variation of OL with temperature could be affected simultaneously by pressure in analogy with the observations made by Kotousov. Waldmann 6). however, raised objections against the interpretation of the Kotousov results by a pressure dependent thermal diffusion factor. He suggested that a thermal effusion mechanism could produce effects similar to the observed ones, if in the experimental apparatus the connection tube between the hot and the cold volume was filled up with some porous material.

Fig. 1. Apparatus

for- the measurement of the shift in concentration diffusion

-

621 -

‘by thermal

622

W. VAN DAEL,

A. VAN ITTERBEEK

AND H. CAUWENBERGH

mA

Fig. 2. The heating current in the analyser as a function of pressure for two He-Ar mixtures

Fig. 3. The thermal diffusion factor for a He-Ar

mixture as a function of pressure

In order to clarify to some extent the remaining uncertainty, new measurements have now been made of the thermal diffusion factor in the range 1 < p < 400 torr. The experimental conditions are taken similar to those of the Kotousov experiment. .A two-bulb apparatus (fig. 1) is filled, at a uniform temperature Tl, with a He-Ar mixture (50.05% Ar). The temperature of the upper volume (VI = 500 ems) is in-

THERMAL

DIFFUSION

FACTOR

FOR PRESSURES

UP TILL

400

TORR

623

creased up to T1 = 333°K while the temperature of the lower one (Vs = 1 ems) is kept constant at Ta = 294°K. Thermal diffusion produces a shift in concentration which as a result of the large value of Vi/ Va affects almost solely the composition in Vs. A thermal conductivity gas analyser is incorporated in Ve: a bead thermistor, surrounded by a small heating coil (overall diameter 2 mm), is kept at a constant temperature (298’K) by regulating the power dissipated in the coil. So the heating current I depends on the effective thermal conductivity of the gas which is a function of the composition and of the pressure. In fig. 2 are given the calibration curves I (p) for He-Ar mixtures with respectively 50.05% and 51.22% Ar. The electrical measuring system has such a resolution that changes in concentration of 0.01 o/0 can be detected. For the lowest p values the sensitivity decreased slightly. The final concentration in Vs after thermal diffusion is very close to that of the second calibration curve (51,22%) : in order to evaluate small deviations a linear relation is used between AI2 and the changein concentration AC. The function 12(c) has been checked over a wider range of concentrations (45-53% Ar) without an appreciable deviation from linearity. When the volume Vi is heated up from the initial temperature Ti to Ti the total pressure in the apparatus rises from pi to 9,. Due to the fact that the total volume is only slightly larger than Vi one obtains in good approximation PC/p, = Tl/Tt. It is quite important to take this increase in pressure into account because the equilibrium heating current is also a function of pressure. It turns out that the I(p) curves at constant concentration can be represented in a simple form by 1

-=a++ I2 - I;

b

P

with a and b constants and 10 the equilibrium heating current at very low pressure, which gives information about the amount of heat transferred by other means than the thermal conductivity of the gas. This relation makes it easy to correct the initial current reading I (50.05%, pg) into I’ (50.05°/0, p,) which can then be compared with the final reading I (x ,pe). The experimental data on the thermal diffusion factor are given in fig. 3 for the pressure range 1 ( p ( 400 torr: all measuring points give a value constant to within 5%, exception made for a few points with p < 10 torr where the scattering is somewhat larger. In the same graph Kotousov’s data are represented by the full line. Recently Mason and Malinauskas 6) have worked out theoretically Waldmann’s suggestion of thermal effusion in the Kotousov experiment; they showed that his results can be made plausible if one assumes that in his experiment a connection tube is used with a mean pore size of 5 microns. We take the opportunity to express our truly thanks to the “Fonds voor Fundamenteel Collectief Wetenschappelijk Onderzoek”, which has financially supported this research. Received lo- 12-65 W. A. VAN

VAN

DAEL

ITTERBEEK

Ii. CAUWENBERGH

Instituut vool lage temperaturen en technischeFysica, Leuven, Belgie

624

THERMAL

DIFFUSION

FACTOR FOR PRESSURES

UP TILL

REFERENCES

1) Beckey, H. D. and Groth, W. E., Z. Naturforsch. 7a (1952) 474. 2) Becker, E. W., Z. Naturforsch. 5a (1954) 457. L. S., Sovjet Phys. - Techn. Phys. 7 (1962) 159. 3) Kotousov,

4) Neal, W. E., Proc. Phyq. Sot. 82 (1963) 333. L., Z. Naturforsch. 18a (1963) 417. 5) Waldmann, A. P., J. them. Phys. 41 (1964) 3815. 6) Mason, E. A. and Malinauskas,

400 TORR