Production of Low Temperatures by F. Simon’s Method

V. G. Fastovsky, Moscow

The study of the physicochemical properties of matter at low temperatures is limited by the circumstance that obtaining temperatures below \(70^\circ\mathrm{K}\) presents a very difficult technical problem.

A very simple method for lowering the temperature of gases is the cascade method of Pictet, which, unfortunately, is unsuitable for liquefying hydrogen; this is explained by the presence of temperature gaps in the regions \(N_2\)—\(H_2\) and \(H_2\)—He: the boiling point of liquid nitrogen is \(77.31\,\mathrm{K}\) \((P = 1\,atm)\), while the critical temperature of hydrogen is \(33.2\,\mathrm{K}\); correspondingly, the boiling point of hydrogen is \(20\,\mathrm{K}\), and the critical temperature of helium is \(5.25\,\mathrm{K}\).

The temperature gaps noted above for the regions \(N_2\)—\(H_2\) and \(H_2\)—He can be sharply reduced by intensive pumping of liquid nitrogen or liquid hydrogen—by such a method (let us call it the condensation method) one can introduce, for the region \(N_2\)—\(H_2\), a temperature gap down to \(28\)--\(30^\circ\), and for the region \(H_2\)—He—down to \(4^\circ\).

To broaden the range of application of Pictet’s cascade method in the region of temperatures below that of liquid nitrogen, and to fill the temperature gaps between \(N_2\)—\(H_2\) and \(H_2\)—He, F. Simon1 proposed an original method for obtaining low temperatures, which is based on the utilization of the negative thermal effect of gas desorption; in the cascade method of lowering the temperature of gases the heat of evaporation is used, whereas in F. Simon’s method it is the heat of adsorption.

Fig. 1.

The essence of F. Simon’s desorption method is easily understood from consideration of the schematic diagram of the apparatus (Fig. 1): the adsorbent (activated charcoal) is degassed in a hard-glass bulb \(B\) at a temperature of \(400\)--\(500^\circ\mathrm{C}\), with pumping off of the gases evolved, and is then poured into vessel \(A\). Space \(D\)—an extension of vessel \(A\)—is thoroughly evacuated and, together with vessel \(A\), is placed in vessel \(E\), which is immersed in a bath of liquid nitrogen or liquid hydrogen.

V. G. FASTOVSKII

When hydrogen or helium is adsorbed by activated charcoal, a thermal contact is created between the bath of liquid nitrogen (or hydrogen) and vessel \(A\) by introducing hydrogen or helium into space \(f\); above the bath of liquid nitrogen (or liquid hydrogen) a deep vacuum is produced, and at the same time the process of adsorption of \(\mathrm{H_2}\) or He by activated charcoal takes place. The heat of adsorption is removed through the thermal contact of space \(f\) into the refrigerant bath.

After the adsorption process is completed, space \(f\) is thoroughly evacuated, and adsorber \(A\) becomes thermally insulated; then follows the process of desorption—pumping the gas out of the adsorbent by a powerful vacuum pump, which leads to a lowering of the temperature in the adsorber.

When the temperature in the adsorber reaches \(4.0\)–\(4.5^\circ\mathrm{K}\), helium is introduced through a tube into vessel \(K\); it condenses on the walls of the tube and flows down into vessel \(K\).

This method does not require a compressed gas, complicated constructions, and, provided liquid nitrogen or liquid air—now very readily available—is present, it makes it possible in principle to liquefy hydrogen, and, provided liquid hydrogen is present, to liquefy helium.

Among the first studies by F. Simon and Lange\(^{2}\), which carried out experiments with 15 g of charcoal, should be noted for covering the temperature interval \(\mathrm{H_2}\)—He; the initial desorption temperature (\(T_H\)) (the temperature of the liquid-hydrogen bath) was equal to \(13^\circ\mathrm{K}\), and the pressure over the charcoal (before desorption) was \(1.3\ \mathrm{atm}\); a few seconds after the beginning of helium desorption from the adsorbent the temperature reached \(7^\circ\mathrm{K}\), and then \(4^\circ\mathrm{K}\)—this temperature was maintained constant for about 5 hours, which is of great importance for the thermostat.

Extensive work in the \(\mathrm{H_2}\)—He region was carried out by K. Mendelssohn\(^{3}\), who liquefied helium by the desorption method and performed a series of interesting investigations of heat capacities at the temperature of liquid helium and below—down to \(2^\circ\mathrm{K}\).

E. Justi\(^{4}\) believes that, since K. Mendelssohn worked with an elevated pressure over the charcoal (\(7\)–\(8\ \mathrm{atm}\)), the principal cooling effect should be attributed to the work of expansion, while the heat of adsorption is of secondary importance in these experiments.

De Haas and his collaborators\(^{5}\) carried out extensive investigations of the electrical conductivity of metals at low temperatures; for the temperature range \(4.2\)—\(14^\circ\mathrm{K}\) they used the desorption method.

It may be asserted with certainty that for the temperature interval \(\mathrm{H_2}\)—He the desorption method justifies itself and gives acceptable results.

The situation is more complicated with the second, wider temperature interval.

E. Justi persistently sought to liquefy hydrogen by the desorption method—in his first experiments he barely reached \(48^\circ\mathrm{K}\) (initial pressure—\(1\ \mathrm{atm}\)), and in subsequent experiments with two-stage desorption he covered the temperature range from 58 to \(35^\circ\mathrm{K}\). E. Justi came to the conclusion that hydrogen cannot be liquefied by the desorption method.

In this connection it should be recalled that, when hydrogen is adsorbed by charcoal at the temperature of liquid hydrogen, the transition of orthohydrogen into parahydrogen takes place,\(^{7}\) which has an adverse influence on the refrigerating effect of the desorption method for obtaining low temperatures.

It seems advisable to elucidate in somewhat greater detail the essence of the desorption method of obtaining low temperatures: in the presence of a condensate we operate with a monovariant system, whereas in the desorption method one can freely operate with an additional variable—the amount of adsorbed gas, i.e., here there is no single-valued dependence between pressure and temperature.

For a condensate, the relation between \(T\) and \(p\) is given by the Clausius–Clapeyron equation

\[ \frac{d\ln p}{dT}=\frac{\lambda}{RT}. \tag{1} \]

We now have the possibility of pumping liquid nitrogen or liquid hydrogen down to \(1\) mm absolute pressure; when the pressure above the condensate is reduced from \(1\) atm to \(1\) mm Hg we obtain the corresponding ratio \(T_k\) (at \(p=1\) atm) to \(T_k\) (\(p=1\) mm Hg), which can be expressed as follows\(^8\):

\[ K=\frac{T_k}{T_n}=\frac{A}{A+12}, \tag{2} \]

where \(A\) is Trouton’s coefficient, \(T_n\) is the boiling temperature at \(p=1\) atm, and \(T_k\) is the final temperature at \(p=1\) mm Hg. If we take the normal value \(A=22\), then from equation (2) we obtain the following relation:

\[ T_k=K T_n=0.65T_n. \tag{3} \]

Curve \(a\) in Fig. 2 gives interpolated values of \(A\) as a function of temperature\(^8\).

The lower the boiling temperature \(T_n\), the wider the temperature region covered for the same ratio of initial and final pressure (\(1\) atm—\(1\) mm Hg)—the coefficient \(K\) will decrease. Thus, F. Simon gives the following data: for nitrogen we obtain \(T_k=0.59T_n\), for hydrogen \(T_k=0.47T_n\), and for helium \(T_k=0.28T_n\).

In accordance with the data given, it is possible, when pumping down to \(1\) mm Hg absolute pressure above the condensate (initial pressure \(p=1\) atm), for nitrogen to cover the temperature range from \(77\) to \(46^\circ\) K, for hydrogen—from \(20\) to \(9.5^\circ\) K, and for helium—from \(4.2\) to \(1.2^\circ\) K.

Fig. 2.

Curve \(b\) in Fig. 2 gives the corresponding values of

\[ K=\frac{T_k}{T_n} \]

as a function of \(T_n\).

TABLE 1

What will be the corresponding values of

\[ K=\frac{T_k}{T_n} \]

for the desorption method?

The investigations mentioned above by F. Simon, Gaaz, Mendelssohn, and others make it possible to say that for the region \(\mathrm{H_2}\)—He the desorption method is almost equivalent to the condensation method—at the corresponding pressure drop it gives values of \(K\) approaching those presented in Fig. 2 (curve \(b\)).

For the temperature range \(\mathrm{N_2}\)—\(\mathrm{H_2}\), one should point to the systematic investigations of A. Interbeck and his collaborators\(^9\).

The first experiments on the adsorption of \(\mathrm{H_2}\) and its subsequent desorption gave the following results (Table 1). The authors, unfortunately, do not give the valu-

\(^1\) Let us recall that Keesom attained a temperature of \(0.7\) K by reducing the pressure above liquid helium to \(0.004\) mm Hg.

...of the final pressures corresponding to the final temperatures; their results give an average cooling of 23° and are very far from the critical temperature of H₂.

The initial pressure has a great influence on the refrigerating effect of the subsequent desorption.

At an initial pressure of 4.56 atm and an initial temperature of 91.7 K, A. Interbeck et al. reached a final temperature of 53.4 K—lower than the temperature 38.3.

TABLE 2

For an exact thermodynamic judgment of F. Simon’s desorption method, it is necessary to know the heats of adsorption of hydrogen (and helium). These investigations for hydrogen were carried out by A. Interbeck and V. Dingenen in the temperature interval 90–50° K.

From these data, the above-mentioned investigators calculated, by the Clausius–Clapeyron equation, the heats of adsorption \(q\) of 1 g-mole of hydrogen; Table 2 gives the heats of adsorption \(Q\), referred to 1 g of activated carbon at a final pressure of H₂ over the carbon of 60 cm Hg. The data presented show a decrease in the heat of adsorption with increasing pressure over the carbon, and, at constant pressure, a decrease in the heat of adsorption with decreasing temperature.

At the same time, A. Interbeck and V. Dingenen carried out experiments on the desorption of hydrogen; Table 3 lists the experimental and calculated quantities. The quantities in columns 5 and 7 of Table 3 show large discrepancies, which, evidently, should be attributed to the penetration of heat into the apparatus from outside.

TABLE 3

The best results of the experiments of A. Interbeck and V. Dingenen give the value \(K=\dfrac{T_k}{T_n}=0.59\) (pressure drop \(1\) atm—\(1\) mm Hg), which is considerably worse than the data given above for the compensation method.

An increase in the efficiency of the desorption method can be achieved by taking account of the following factors:

1. Selection of the type of activated carbon; the adsorbent should give a minimal increase in the heat of adsorption with decreasing pressure (for the interval 70 cm Hg—1 mm Hg).
2. Provision of maximum pumping speed during desorption.
3. Carrying out the adsorption process at a pressure above one atmosphere.

A. Interbeck and V. Dingenen believe that, at an initial temperature of 67° and a pressure of 2.5 atm, it is possible during subsequent desorption to reach the critical temperature of H₂.

It must, however, be agreed with E. Justi that, if one operates with higher pressures (7–8 atm), there is no basis for attributing the entire refrigerating effect to the heat of adsorption.

1. The initial temperature—before desorption—must be lowered to a minimum by corresponding pumping of liquid nitrogen or liquid hydrogen.

Undoubtedly, the desorption method for obtaining low temperatures considered by us cannot, in its technical significance, be compared with the methods of Linde—Onnes and Claude—Kapitza.

The significance of the desorption method is more limited—this method is of great importance for obtaining a constant temperature medium (thermostat), which has been confirmed by the studies of E. Oschl in the region \(N_2\)—\(H_2\), and of Giauque and others in the region \(H_2\)—\(He\).

References

1. F. Simon, Physik. Z., 27, 790, 1926; Z. Gesamte Kälte Indust., 34, 217, 1927; Z. Physik, 87, 815, 1934.
2. F. Simon and F. Lange, Z. physik. Chem. B 16, 72, 1931.
3. K. Mendelssohn, Z. Physik, 73, 482, 1932.
4. E. Justi, Z. Physik, 87, 273, 1934.
5. W. U. de Haas, U. G. de Boer, J. van den Berg, Physica I, 609, 1934; Physika II, 433, 1935; III, 440, 1936; IV, 683, 1937.
6. E. Justi, Ann. Physik, 9, 570, 1931; Z. Physik, 87, 273, 1934.
7. A. Eucken, Naturwiss., 17, 182, 1929.
8. F. Simon, Physica, IV, 879, 1937.
9. A. van Interbeek and W. Vereyeker, Physica, III, 666, 954, 1936; A. von Interbeek and W. von Dingenen, Physica, IV, 389, 617, 1937.

1. Let us note that the temperature gap between nitrogen and hydrogen can be partially covered by a neon cycle. ↩