ISOTHERMAL THROTTLING EFFECT OF GASES

Apparatus for Measuring the Isothermal Throttling Effect

KURIN N. P.

Introduction

The Joule–Thomson effect, as well as the isothermal throttling effect for certain gases, for example carbon monoxide and gas mixtures, has not yet been determined experimentally, although such measurements are desirable from both theoretical and practical points of view.

Knowing the Joule–Thomson effect or the isothermal throttling effect over a large range of pressures and temperatures, one can construct diagrams characterizing the states of gases and their mixtures (the differential effect as a function of pressure and temperature; enthalpy—temperature; heat capacity \(C_p\)—temperature; \(C_p\)—pressure; temperature—entropy; enthalpy—entropy; \(PV, P, <\)), which make it possible to determine a number of quantities of great importance both for theory and for the technology of deep cooling, for example, heat capacity, enthalpy (heat content), entropy, \(PV\), and others.

Joule–Thomson Effect [1]

Until now, the Joule–Thomson effect has been most widely used for constructing \(i—T—P\) diagrams. As is known, this effect consists in the fact that, during the adiabatic expansion of a real gas without the performance of external work, a decrease occurs—and sometimes, depending on the selected throttling conditions, an increase—in temperature.

Two Joule–Thomson effects are distinguished, namely: the differential and the integral effects.

The first is the ratio of an infinitely small change in the temperature of a gas (most often a decrease in temperature) to an infinitely small adiabatic drop in its pressure without the performance of external work, and is defined by the following equation:

\[ L_i=\left(\frac{\partial T}{\partial p}\right)_i, \]

where \(L_i\) is the differential Joule–Thomson effect,
\(T\) is the absolute temperature of the gas,
\(p\) is the gas pressure,
\(i\) is the enthalpy.

In practice, the differential effect is understood to mean the change in the temperature of a gas when it is throttled by 1 atm.

The integral Joule–Thomson effect is the change in the temperature of a gas over large pressure-drop intervals and is calculated by integrating the equation

\[ T_2 - T_1 = \int_{P_1}^{P_2} \alpha_i\, dp = \int_{P_1}^{P_2} \left(\frac{\partial T}{\partial p}\right)_i dp, \]

where \(T_1\) and \(T_2\) are, respectively, the initial and final temperatures of the gas during throttling.

For theory and engineering, the differential Joule–Thomson effect is of great importance, since it makes it possible to determine the dependence of enthalpy on pressure and to construct the diagrams indicated above.

Technique for Measuring the Joule–Thomson Effect

The first attempt to determine the change in the internal energy of a gas as a function of the change in volume belongs to Gay-Lussac [2]. In 1806 the latter published the results of his work in this direction. The experiments were carried out as follows: two vessels, each of 12 liters capacity, connected by a tube with a stopcock (Fig. 1), were thoroughly dried and evacuated. Then one of the vessels was filled with air. After the temperatures had equalized, the stopcock \((K)\) was opened, and the gas (air) from vessel \((A)\) partially passed into vessel \((B)\). At the same time the change in temperature in each of the vessels was measured. These experiments showed that the drop in temperature in vessel \(A\) corresponded exactly to the rise in temperature in vessel \(B\).

Fig. 1. Gay-Lussac apparatus

Thirty-nine years later, in 1845, Joule [3], measuring temperatures with great accuracy (to \(0.003^\circ\text{C}\)), repeated Gay-Lussac’s experiments. The experiments were carried out in two variants (Figs. 2 and 3). In the first variant, vessels \(A\) and \(B\) were placed in a common water calorimeter. Vessel \(A\) was filled with gas up to 22 atm, and then, after the temperatures in the calorimeter had equalized, the gas was admitted through the stopcock \((K)\) from vessel \(A\) into vessel \(B\). As a result of these experiments it was found that the temperature of the calorimeter remained unchanged.

Fig. 2

Fig. 3

In the second variant, vessels \(A\) and \(B\) were placed in different calorimeters. However, during the expansion of the gas, just as in Gay-Lussac’s experiments, the drop in temperature \((2.36^\circ\text{C})\) in vessel \(A\) was equal to the rise in temperature \((2.38^\circ\text{C})\) in

vessel \(B\). On the basis of his experiments, Joule came to the conclusion that the internal energy of a gas does not depend on volume, i.e.

\[ \left(\frac{\partial U}{\partial V}\right)_T = 0. \]

To verify the proposition that the internal energy of a gas does not depend on volume, Gay-Lussac [4] carried out experiments according to the following scheme (Fig. 4).

In the parts of the tube \((A)\) and \((B)\), separated by a gas-impermeable membrane \((v)\), there was air at atmospheric pressure, so that in this position the manometer \((m)\) indicated zero. Then, after disconnecting the manometer by means of the stopcock \((h)\), the air from \((A)\) was pumped into \((B)\) until the pressure in \((B)\) became equal to 1.5 atm, and in \(A\) only 0.5 atm.

Fig. 4.

Next, by a rapid motion of the whole tube, the ball \((S)\) tore the membrane \((v)\), and the pressures in \((A)\) and \((B)\) became equalized; at the same time the manometer \((m)\) was again connected with chamber \((B)\). The change of temperature that was assumed in this case, owing to the expansion of the air, should have immediately caused a change of pressure; however, this did not occur, since the manometer still indicated the initial pressure in the tube.

However, despite these unsuccessful attempts to find a dependence of the internal energy of a gas on volume, in 1852 Thomson, together with Joule [5], again carried out experiments to test Joule’s law

\[ \left(\frac{\partial U}{\partial V}\right)_T = 0, \]

but, unlike the previous investigators, they used a dynamic method. They forced the gas to pass in a continuous stream through a tube (Fig. 5), inside which was placed a throttling porous plug made of cotton wool or silk; as a result, a definite pressure difference was established on the two sides of the plug. To prevent heat exchange with the surroundings, the tube \((b)\) was made of a material with poor thermal conductivity (wood); in addition, it was covered with a thick layer of silk insulation. The temperature of the gas before the plug and after it was measured by means of mercury thermometers. The experiments were carried out at constant temperatures from 4 to \(100^\circ\)C and at pressures before the plug of up to 4.5 atm and after it of 1 atm. It was found that, in the investigated range of temperatures and pressures, most gases (air, oxygen, nitrogen, and carbon dioxide) lower their temperature upon throttling, and only hydrogen raises it. Thus, by these classical experiments

It was established by Joule and Thomson that the internal energy of a real gas also depends on volume, i.e., in the general case

\[ \left(\frac{\partial U}{\partial V}\right)_T \ne 0 . \]

Subsequent numerous studies by other authors investigated the indicated phenomenon of the change in gas temperature during throttling for most of the most important gases (air, oxygen, nitrogen, carbon dioxide, hydrogen, helium) over a wide range of temperatures and pressures. Without dwelling in detail on the results of these works, we shall note only that the Joule–Thomson effect depends both on the pressure and, to a large extent, on the initial throttling temperature. Readers interested in this question are referred to the specialized literature [6].

Fig. 5.

Fig. 6.

Installations for measuring the Joule–Thomson effect may be divided into three types according to the nature of the throttling devices used in them. In the first, a porous plug placed in a tube made of a material with poor thermal conductivity is used as the throttle.

In the second type, the porous plug is replaced by a cylindrical porous porcelain tube, so that the throttled gas passes in the radial direction toward the axis of the outer tube carrying the pressure.

And finally, the third type is a narrow aperture of variable size, i.e., a valve.

The newest throttling device, having a plug as the throttle, was proposed by Hausen [6] and others [7] [8].

The construction of Hausen’s throttling device is shown in Fig. 6. The body of the apparatus \((a)\) and the inner tube \((b)\) are made of Siemens-Martin steel. On the outside, the body of the apparatus is surrounded by a copper coil—

…with [felt], enclosed in a lead jacket serving as a metallic thermostat. The inner part of tube \((b)\), to prevent heat exchange, is lined with wood. The throttle plug is made of felt and on the sides is covered with a layer of soft rubber. The temperature before and after throttling was measured by means of two platinum resistance thermometers \((P)\).

The air subjected to throttling was led into the coil \((a)\), where, at the expense of the cold of the already throttled air, it was cooled to the required temperature and then, through the interwall annular space formed by the wall of the body \((a)\) and the tube \((b)\), washing over a platinum resistance thermometer, reached the throttle plug \((i)\). Further, the gas, passing through the plug \((i)\), was throttled and, washing over the second resistance thermometer, passed into the coil \((j)\), in which it gave up cold to the fresh air flowing toward it.

At the same time, simultaneously with the temperature measurement, the pressure difference was measured with a special mercury differential manometer; from the data obtained the Joule–Thomson effect was determined.

A second type of throttle apparatus is the apparatus (Fig. 7) proposed by Burnett and Roebuck [9]. This apparatus consists of a metal jacket \((C)\), which is insulated inside by a thick layer of heat-insulating

Fig. 7.

material \((N)\), and of a porous throttling porcelain tube \((P)\). Gas at a definite temperature, washing over the resistance thermometer \((T_1)\), then passed in the radial direction through the porcelain tube \((P)\), where it was throttled, and then, washing over the second resistance thermometer \((T_0)\), left the throttle apparatus.

A great shortcoming of this type of apparatus is that, owing to the small thickness of the porous porcelain tube \((\sim 1\ \mathrm{mm})\), and consequently its relatively high thermal conductivity, it is difficult to conduct the throttling process adiabatically, which leads to large errors.

An example of the third type of throttle apparatus is the throttle valve shown in Fig. 8, used by Wrede and Heuse [10]. In order to reduce heat exchange with the surroundings to a minimum, this valve is made of vulcanized fiber. To provide sufficient mechanical strength, the valve is equipped with a metal jacket. The spindle \((S)\), serving to regulate the degree of throttling, for the sake of proper strength was made of metal, but its continuation outward was made of wood, as a result of which heat exchange through the spindle was reduced to a minimum. The entire throttle apparatus was carefully insulated with hair felt. The temperatures before and after throttling were measured with platinum resistance thermometers.

In all three apparatuses the initial temperature of the gas was attained either by means of the cold of a cryostat or by heat exchange with the throttled outgoing gas.

Of the types of throttling apparatus described, the one that most satisfies the high requirements of accuracy is the apparatus in which a plug serves as the throttle. It was precisely with such an apparatus that Hausen achieved a high accuracy (1%) in measuring the Joule–Thomson effect for air. The reason for this is that, owing to the great thickness and poor thermal conductivity of the material of the plug, and also to the good insulation of the inner tube (b) by wood (Fig. 6), the throttling process most closely approaches an adiabatic process, and therefore it is possible with great accuracy to measure not only the integral but also—what is especially important—the differential Joule–Thomson effect.

The use of porcelain tubes as a throttle did not give positive results, since the errors caused by the deviation of the throttling process from the adiabatic process are too large. Thus, for accurate measurements of the differential Joule–Thomson effect the indicated type of throttle is not suitable.

Fig. 8.

However, by using good external insulation and working with high gas velocities, porous porcelain tubes may prove suitable for measuring the integral throttling effect, since in this case the heat losses per unit of gas passed will be small. On the contrary, the throttling valve, in comparison with porcelain tubes, proved more suitable.

All the types of throttling apparatus considered possess a common drawback connected with heat losses due to operation with temperature differences, namely that in order to obtain sufficiently accurate results it is necessary to work with gas velocities that are extremely high for laboratory conditions.

Thus, in the most accurate measurements of the differential Joule–Thomson effect for air, it was necessary to pass 2000 moles of gas per hour through the throttle (i.e., 44.8 m³/hour). This latter circumstance, besides making it necessary to use powerful compressors, is associated with difficulties in the investigation of rare and expensive gases (He, Ar, etc.), which in this case are required in considerable quantities.

All these shortcomings are to a considerable degree eliminated in the study of the isothermal throttling effect.

Isothermal Throttling Effect

By the isothermal throttling effect is understood that infinitesimally small quantity of heat which must be supplied to one mole of gas, at a given pressure and temperature, in order exactly to compensate the fall in temperature that occurs as a result of an infinitesimally small pressure drop.

of gas without the performance of external work. Thermodynamically, the isothermal throttling effect is defined by the following equation:

\[ \left(\frac{\partial i}{\partial p}\right)_T=\beta . \]

where \(i\) is the enthalpy of the gas,
\(p\) is the pressure,
\(T\) is the absolute temperature,
\(\beta\) is the isothermal throttling effect.

By analogy with the Joule–Thomson effect, the effect under consideration may be divided into the differential isothermal throttling effect, characterized by the equation given above, and the integral isothermal throttling effect, defined by the equation:

\[ i_2-i_1=\int_{P_1}^{P_2}\beta\,dp =\int_{P_1}^{P_2}\left(\frac{\partial i}{\partial p}\right)_T\,dp \]

However, for constructing \(i\)—\(T\)—\(P\) diagrams, the differential isothermal throttling effect is of greater importance.

The differential Joule–Thomson effect is related to the differential isothermal throttling effect by the following equation:

\[ \left(\frac{\partial i}{\partial p}\right)_T = -C_p\alpha_i = -C_p\left(\frac{\partial T}{\partial p}\right)_i, \]

where \(C_p\) is the true heat capacity of the gas at constant pressure.

In 1903 Buckingham [11] made the first attempts at a rough determination of the isothermal throttling effect. The apparatus described by the author consisted of a tube with a porous plug placed inside it, in which a heating winding was located. The decrease in the temperature of the gas occurring during its expansion in the plug was compensated by the heat released by the heated coil, so that the temperature of the gas before throttling and after it remained constant.

Somewhat later, Roebuck [12] determined the isothermal throttling effect of carbon dioxide. He started from liquid \(CO_2\), which, in a definite amount, was placed in a small steel cylinder \(P\) (Fig. 9). The carbon dioxide, evaporating, first passed through an orifice \(O\), the size of which could be varied at will by means of a screw \(S\), then entered the copper vessel \(K\) surrounding the cylinder, and from there passed out through the coil \(R\). Thermometers \((T_1)\) and \((T_2)\) served to observe the equality of the temperatures of the calorimeter and of the gas leaving the coil. The heat given up by the calorimeter to the throttled carbon dioxide was compensated by the heat of an electric heater.

In this case, in order to obtain the isothermal throttling effect of gaseous carbon dioxide during its expansion from the pressure \(P_s\), equal to the vapor pressure at the given experimental temperature, to the final pressure \(P_o\), it is necessary to subtract the heat of vaporization from the total amount of heat expended per mole of gas.

An apparatus for accurate measurements of the isothermal throttling effect at various temperatures and pressures was described in 1932 by Eucken and co-workers [13], [14]. Using this method, they measured the isothermal throttling effect of methane at pressures from 10 to 110 atm and temperatures from \(+20\) to \(-108^\circ\) C.

On the basis of the results of this work, \(i\)—\(T\)—\(P\) diagrams were constructed for methane, whose accuracy, in any case, is not less than the accuracy

analogous diagrams for air, compiled by Hausen on the basis of his measurements of the differential Joule–Thomson effect.

The principle of measuring the isothermal throttling effect consists in the following. The gas under investigation, at a given temperature and pressure, passing through a throttle valve, expands to a certain final pressure, and the cooling of the gas that occurs in this process, as a result of the Joule–Thomson effect, is exactly compensated by the heat released by an electric current passing through a heating wire placed inside the throttle valve. Thus, knowing the absolute pressure of the gas before and after the throttle, as well as the pressure difference, the gas velocity, and the amount of heat supplied, one can calculate the isothermal throttling effect at the given temperature and the given (mean) pressure. The only drawback of this method, as compared with the method of determining the Joule–Thomson effect, is that, besides the pressure difference and observations along the isotherm, it is also necessary to measure a third quantity—the gas velocity, whereas for the Joule–Thomson effect it is necessary to know only the pressure difference and the temperature difference. However, this drawback is outweighed by the much greater advantage that, thanks to working by the isothermal method, i.e. at constant temperature, all heat losses associated in the Joule–Thomson effect with the temperature difference are reduced to a minimum. As a result, it becomes possible to make accurate measurements with quantities of gas many times smaller than those required for accurate measurements of the Joule–Thomson effect. Thus, for example, with approximately the same accuracy, Eucken and his collaborators used an amount of gas about 200 times smaller than that used by Hausen. This latter circumstance makes it possible to carry out accurate measurements of the isothermal throttling effect and, consequently, to construct \(i\)—\(T\)—\(P\) diagrams with gases that are available only in small quantities.

Fig. 9.

Moreover, in such measurements there is also no need to use powerful compressors, which can successfully be replaced by laboratory compressors and ordinary cylinders with compressed gases.

The advantages described above prompted us, in investigating the isothermal throttling effect, to adopt this method.

Arrangement of the Apparatus

Dry gas, purified of foreign impurities, from cylinders (5, Fig. 10) was directed through a fine-control valve (6) into a copper coil (8). The latter, together with a copper cup (9), was placed in the liquid of the cryostat (7). On passing through the coil, the gas was cooled to the temperature of the cryostat and then entered the [device] located inside the cup.

Fig. 10.

a throttle valve, in which it was throttled to 4.5 atm with simultaneous compensation of the cooling by heating with the aid of an electric current. After throttling through the second valve, with fine adjustment (14), the gas entered one of two previously calibrated gasometers (17), by means of which the rate of the gas flow was measured.

From the line supplying the gas to the throttle and carrying it away from the throttle, two tubes branch off; these are connected to steel-tube manometers (10), intended for measuring the absolute pressure of the gas before and after the throttle, and also to the high- and low-pressure limbs of the differential manometer (12).

From the gasometers (17) the gas, by means of the compressor (1), through the oil separator (2), the cooler (water–ice) (3), the dryer filled with solid caustic soda, and the decarbonizer (4), was again directed into the cylinders (5).

Construction of the throttle valve

The throttle valve (Fig. 11) consists of a separable hollow copper cylinder (1), inside which there is a second cylinder (3), a throttle seat (4), and a throttle needle (5). On the throttle seat is placed

Fig. 11

a cylinder (7) glued by means of shellac from several layers of mica, on which the heating coil (12) is wound. The heating coil is made of thin constantan wire \((d = 0.07\ \mathrm{mm})\), whose total resistance is about 60 ohms. The ends of the heating coil were welded by means of an electric spark to insulated copper leads, which were brought out through tube (8) to the source of electric current. Tube (8), after leaving the cryostat, was sealed with picein. After the heating coil had been wound and the copper leads soldered to it, both parts of the throttle apparatus (1) and (2) were screwed together and, for complete tightness, soldered with tin. Tubes (8), (10), (11), made of iron, were also soldered with tin.

The gas enters through tube (10), is throttled in the throttle seat (4), and, for better heat transfer, passes helically along the threading of the steel—

nozzle needle (5); then the gas washes over the coil (12), heated by an electric current, as a result of which its temperature, having decreased owing to throttling, again rises to its initial value. For better equalization of the temperature, the gas is passed through the wall space (13), and then through the iron tube (11) it is directed into the gasometer. To ensure the most rapid equalization of temperatures, all parts of the throttle valve, with the exception of the brass throttle seat (4) and the steel needle (5), are made of red copper.

Eucken points out that in his experiments with air, when identical temperatures of the entering and leaving gas were attained, the body of the throttle valve was heated somewhat above the temperature of the cryostat; therefore appreciable heat losses by radiation could have arisen, which would have led to significant errors. Therefore, in order to reduce these errors to a minimum, the surface of the throttle valve was carefully polished.

To regulate the degree of throttling, each time it is necessary to unsolder the plug (14) on the gas-outlet tube (11) and, through the opening thus formed, to screw the steel needle (5) in or out with a screwdriver. In his last work Eucken [14] used a worm gear to set the needle to the required degree of throttling; with its aid the throttle can be adjusted from outside without dismantling the apparatus. However, we refrained from using such a device, since it would have to reduce the accuracy of the results obtained, owing to heat loss by the throttle valve through the metal parts of the worm gear.

Arrangement of the measuring apparatus in the vessel

Figure 12 shows the arrangement of the measuring apparatus in the vessel.

Gas at the temperature of the cryostat enters tube (15), which at its lower end is provided with an enlargement (4). The thermoelement (b), placed inside tube (15), serves to monitor the temperature of the incoming gas; the other end of this thermoelement is placed in a copper sleeve (7), so that with this thermoelement it is possible to determine how much the temperature of the incoming gas differs from the temperature of the cryostat. The gas then passes through the enlarged part of the tube (4), inside which one end of the compound ten-junction thermoelement (a) is placed; then the gas flows through the throttle valve (1), in which throttling takes place with simultaneous compensation of the cooling, and finally enters the enlarged part of tube (14), inside which the second end of the compound thermoelement (a) is placed. Thus, the actual isothermality of the process is monitored from the readings of the compound thermoelement (a) in the enlarged parts of the tubes through which the gas enters and leaves.

Minimal deviations of the readings of the mirror galvanometer, connected in the circuit of the compound thermoelement, from the zero position, or the complete absence of these deviations, indicate the onset of equality of the temperatures of the incoming and outgoing gas. To monitor the temperature of the outgoing gas, as well as the temperature of the surfaces of the enlarged parts of the tubes and of the throttle apparatus (1), the thermoelements (c) and (e), (d) and (f), respectively, are used.

The second ends of thermoelements (b), (c), (d), (e), and (f), covered with insulation, were placed in a copper sleeve (7) and filled with Wood’s alloy. The copper sleeve was in contact with the liquid of the cryostat and, thus, owing to the good thermal conductivity of copper and Wood’s alloy, the second ends of the indicated thermoelements always had the temperature of the cryostat.

As the insulating material for the second ends of the thermoelements, Bakelite varnish (an alcohol solution) was used. Our earlier attempts to use for this purpose an alcohol solution of shellac proved unsuccessful, since, when the thermoelements were cast with Wood’s alloy, they short-circuited with one another. The copper leads of all the thermoelements listed, before being brought out in the form of a common bundle (12) from the vacuum

Fig. 12

vessel to the measuring apparatus, were each separately packed tightly into one of the grooves of a copper rod (6). The sealing was carried out with shellac and, in addition, to provide strength, the outer part of the groove, after the wire had been laid in it, was covered with a thin layer of fibrous filter paper soaked in shellac.

By means of the indicated device, the incoming copper leads of the thermoelements were brought into good thermal contact with the copper rod; as a result, the heat flowing along these leads from the surroundings was rapidly removed through the copper rod into the liquid of the cryostat, and thus the isothermality was not disturbed. This latter circumstance is of especially great importance when working in the region of low temperatures (below \(0^\circ\text{C}\)).

Sealing the thermoelements \((в)\) and \((f)\), as well as the composite thermoelement \((a)\), in the tubes for the incoming and outgoing gas presented great difficulties. This operation, taking into account the thinness of the wires and the high pressure, required great care and thoroughness of execution, since otherwise it was possible, in addition to poor tightness, to destroy the composite thermoelement.

A large number of substances were tried as sealing putties, but all of them proved of little use for work at high pressures and low temperatures. After prolonged experiments, a reliable method was found for hermetic sealing of the gland type [15].

To determine the pressure difference, thin tubes \((5)\) and \((13)\) branched off from widenings of the incoming- and outgoing-gas tubes precisely at the place of the ends of the composite thermoelement; these tubes were connected respectively with the high- and low-pressure arms of the differential manometer.

Here it is necessary to note that, in the ideal case, the material of the tubes for the incoming and outgoing gas, as well as the material of the tubes leading to the differential manometer and the tube in which the copper leads are brought out of the throttling apparatus, should, in addition to good mechanical properties (strength and flexibility), conduct no heat at all. The latter requirement follows from the necessity of avoiding, as far as possible, extraneous supply and removal of heat from the throttle valve, which would disturb the isothermality. The most suitable metal for this purpose is nickel silver, whose coefficient of thermal conductivity is 25; for lack of nickel silver we used iron, whose coefficient of thermal conductivity, as is known, is approximately twice as large, namely \(=45\text{--}50\). However, iron fully justified itself. All the indicated tubes were soldered to the cup lid with tin. Both the lid and the upper part of the cup \((9)\) are made of iron, which made it possible, without greatly raising the temperature inside the cup, to solder the lid to it.

Measurement of Pressures

The absolute pressures before throttling and after it were measured by means of calibrated steel-tube precision manometers \((10—\text{Fig. }10)\).

The exact measurement of the pressure difference, equal to approximately \(4.5\) atm, was carried out with a mercury differential manometer \((12—\text{Fig. }10)\). In the original design, thick-walled glass capillaries (\(d_{\text{internal}}=1\text{--}2\) mm and \(d_{\text{external}}=14\text{--}18\) mm) were used to observe the mercury level on the high- and low-pressure sides. The capillaries were connected to the steel tubes by means of glands packed with oiled asbestos cord. However, hydraulic testing at pressure of such a differential manometer led to negative results. The capillaries, despite their great thickness, burst at pressures of \(80\text{--}120\) atm.

In this connection we developed a new design of differential manometer, in which the glass capillaries were replaced by contact indicators of the mercury level [16]. A mercury-electric differential ma-

The manometer has two such mercury-level indicators—the upper and the lower. The first is located on the high-pressure leg, and the second on the low-pressure leg of the differential manometer. The operation of such a differential manometer is as follows: under the action of the higher gas pressure, the mercury rises from the high-pressure leg into the low-pressure leg; as it rises, it gradually closes, one after another, the electrical contacts, each of which is connected to a source of electric current and to a small lamp. When the mercury touches a contact, the lamp lights up; this indicates that the mercury level is no lower than that contact. Conversely, at the lower level, as the mercury descends, the contacts open and the lamps go out.

Thus, by knowing which lamp is lit at one level and at the other, one can determine the difference in the heights of the mercury columns and, consequently, calculate the pressure difference. Each level has 40 contacts, spaced 5 mm apart.

The total distance between the first and the last fortieth contact of each level is 195 mm, and thus it is possible to vary the pressure difference within the limits of 390 mm of mercury. The distance between the twentieth contacts of the level indicators is 3411.4 mm. As already indicated, each contact was connected to a separate numbered small lamp (from a pocket flashlight), and the latter were mounted on two common panels corresponding to the upper and lower mercury-level indicators. To supply the lamps, the electric current was transformed from 120 to 4.5 volts (transformer power 100 watts).

The differential manometer used by us makes it possible to measure the pressure difference with an accuracy of up to 5 mm of mercury.

In the work of Hausen, similar measurements were made with an accuracy of 10 mm $Hg$ at a pressure difference of 6.5 atm. Our differential manometer, in addition to its high accuracy, has the further great advantage that it is capable of withstanding high pressures (it was tested at 350 atm), and observation of the level indicators is greatly simplified, since the panels with the lamps can be placed in a convenient location for observation.

When calculating the pressure difference from the mercury-level readings, a correction was introduced for the change in the density of mercury with temperature; for this purpose, in each experiment the temperatures at the top, middle, and bottom of the differential manometer were recorded.

Measurement of the Gas Velocity

The gas velocity was measured by means of calibrated gasometers (Figs. 13 and 14), made of sheet iron. The capacity of each gasometer was 280 liters. Water was used as the hydraulic seal, and a thick layer of machine oil was poured over it. This was necessary to prevent saturation of the gas under investigation with water vapor. Each gasometer was equipped with a thermometer and a mercury manometer. The gasometer bell was balanced by counterweights.

The actual measurement of the gas velocity was carried out by taking readings, at definite time intervals, of an indicator fixed to the gasometer bell and rising together with it along a millimeter scale.

Fig. 13.

Fig. 14.

Visible labels in Fig. 14: “mineral oil”; dimensions: 135, 1200, 540, 580.

Measurement of the Amount of Electrical Energy

The measurement of the amount of electrical energy spent on heating the gas during its throttling, in order to maintain the initial temperature, was carried out by the compensation method. The layout of the apparatus for measuring the electrical energy is shown in Fig. 15.

A battery of lead accumulators served as the current source. To regulate the strength of the heating current, two rheostats were connected in series into the main circuit (\(R\) regul.—Fig. 15). The first of them was an ordinary sliding rheostat, which served for preliminary coarse adjustment of the current strength; the second rheostat, intended for fine adjustment, consisted of a thin graphite rod immersed in mercury. The graphite rheostat made it possible to regulate the heating current smoothly and very accurately. The amount of energy used for heating was determined by measuring the current strength and the voltage drop.

For measuring the current strength, a precision resistance of 10 ohms was connected into the main heating circuit.

The voltage drop across the precision resistance (\(R\) precis.) and across the heating coil (\(R\) heat.) was determined by the compensation method. For this purpose, wires leading to the compensation apparatus branched off from the terminals of the precision resistance (\(R\) precis.) and from the ends of the heating coil. The connection of the compensation apparatus with the precision resistance and with the heating coil was made alternately by means of knife switches. The compensation apparatus itself consisted of a Wheatstone bridge, a standard Weston cell, and 2- and 4-volt accumulators. To measure the voltage drop across the precision resistance, the knife switches (A) were closed, and a 2-volt accumulator was connected into the large circuit of the compensation apparatus by means of a mercury switch. When compensating the voltage drop across the heating coil, the knife switches (B) were closed, and a 4-volt accumulator was connected into the large circuit of the compensation apparatus.

Fig. 15

With complete compensation of the voltage drop, the sensitive zero instrument connected into the small circuit (\(10^{-6}\) ampere) gave no deflection. The voltages of the 2- and 4-volt accumulators were checked with the aid of a standard Weston cell.

Measurement of Temperatures

The high temperatures of the cryostat were measured with the aid of a calibrated standard mercury thermometer. Lower temperatures were measured with toluene and pentane thermometers. As indicated above, to monitor isothermality, and also to determine—

—namely, how much the temperature of the gas entering and leaving the throttle deviates from the temperature of the cryostat—was served by a compound thermocouple (a) and the thermocouples (b), (c), (d), (e), and (f) (Fig. 12). The circuit for connecting the compound and simple thermocouples is shown in Fig. 16. The electromotive force arising as a result of the temperature difference in each thermo-

Fig. 16.

element is transmitted through a switch to a sensitive mirror galvanometer. The deflection of the mirror of the latter is observed through a telescope. In order to achieve greater sensitivity, the scale is placed at a distance of 3 meters from the mirror galvanometer, and the telescope at a distance of 1 m. The scale was curved to a radius of 3 meters, as a result of which the need for corrections to the readings of the mirror galvanometer was eliminated. Each thermocouple was calibrated before being placed in the apparatus. The calibration consisted in determining the defle-

…of the deflection of the mirror galvanometer in scale divisions for a definite temperature difference at the ends of the given thermocouple.

The sensitivity of the single thermocouples \((b)\), \((c)\), \((d)\), \((e)\), \((f)\) was equal to 50 scale divisions per \(1^\circ\) temperature difference, i.e., 1 scale division corresponded to \(0.02^\circ\text{C}\). The sensitivity of the composite tenfold thermocouple \((a)\) was \(0.0018^\circ\text{C}\), and thus, by estimating by eye a tenth of a scale division, it was possible to measure the temperature difference in the widened parts of the tubes of the gas entering and leaving the throttle with an accuracy up to \(0.001^\circ\text{C}\).

To eliminate possible distortions of the thermocouple readings by parasitic electromotive forces, all copper wires connecting the thermocouple with the mirror galvanometer were made from a single piece of wire, and all copper switches were placed in a box covered with a thick layer of wool wadding.

Fabrication of the Thermocouples

All thermocouples were made of copper and constantan. To avoid a large supply of heat from the surroundings, the copper wires of both the simple and the composite thermocouples had a small thickness—\(d = 0.1\) mm.

The constantan wires in the simple thermocouples had a diameter of 0.32 mm, and in the composite thermocouple only 0.07 mm. The use of such thin constantan wires was dictated by the need to make a composite thermocouple consisting of 20 wires of the smallest possible diameter, since otherwise it could not have been inserted and sealed in the narrow gas tubes.

Soldering the ends of the thin copper and constantan wires of the thermocouples caused serious difficulties. The methods tested for this purpose—autogenous welding, as well as welding in the flame of a voltaic arc arising between two graphite electrodes—proved unsuitable for this purpose, since, in addition to strong corrosion and frequent burning-through of the thin wires, the resulting soldered junction heads were too large—0.7 mm.

To overcome these difficulties we developed a method for making the junctions of simple and composite thermocouples by means of an electric spark under water [17]. Using this method, very elegant thermocouples were made with a very small junction head, \(d = 0.2\text{--}0.3\) mm. This latter circumstance was of especially great importance in fabricating the composite thermocouple, since large junction heads would not have allowed it to be inserted into the tube.

The wires of both the simple and the composite thermocouples were covered with a thin layer of shellac. This had to be done both to prevent the individual wires from short-circuiting one another in the composite thermocouple, and to eliminate the possibility of a short circuit of the thermocouple through the body of the gas tubes.

Temperature Regulation and Carrying Out the Experiments

In order to obtain good results in measuring the isothermal throttle effect, it is necessary that the temperature of the cryostat be constant and that its fluctuations not exceed \(\pm 0.05^\circ\text{C}\).

As our experiments showed, obtaining constant temperatures of about \(20^\circ\) and higher is easily achieved with the aid of ordinary electric mercury–toluene thermoregulators and by using intensively stirred water as the thermostat liquid. The \(0^\circ\text{C}\) isotherm was produced with the help of…

by means of a refrigerating mixture of water and ice. In this case the ice, in the form of small pieces, was placed in the mesh cylinder of a mechanical stirrer (1—Fig. 17), as a result of which the possibility of the ice floating up to the surface of the water was eliminated, and the required constancy of temperature over the height of the thermostat was thereby ensured. Low temperatures of the order of \(-180^\circ\mathrm{C}\) were easily obtained with the aid of a bath of liquid oxygen. As for intermediate temperatures from 0 to \(-150^\circ\mathrm{C}\), maintaining their constancy caused the greatest difficulties. After prolonged experiments we succeeded in developing two methods giving satisfactory results. Thus, to obtain constant temperatures from 0 to \(-65^\circ\mathrm{C}\), cryohydrates were used as automatic isothermal compensators of heat exchange between the gas entering for throttling and the liquid of the cryostat. The apparatus necessary for this is shown in Fig. 18. Aqueous solutions of the corresponding salts (KCl, NH\(_4\)Cl, NaCl, MgCl\(_2\), CaCl\(_2\), KOH) of precisely cryohydrate composition were poured into the cryostat (3—Fig. 18) and partially frozen by means of liquid air or oxygen passed through the tube (1—Fig. 18) from a Dewar vessel (2—Fig. 18); at the same time a constant temperature was established in the cryostat, equal to the freezing temperature of the cryohydrate. If the supply of cold was excessive in comparison with the heat introduced by the throttled gas and from the surrounding medium, the layer of solid cryohydrate grew on the tube (1), while if it was insufficient it melted; the imperfection of the regulation of the supply of liquid air changed only the quantity of solid cryohydrate in the cryostat, without affecting the constancy of the temperature of the thermostat liquid. To create a sufficient intensity of heat exchange between the liquid of the bath—

Fig. 17

Fig. 18

with the solid cryohydrate and the metallic parts of the apparatus, intensive stirring of the liquid by a mechanical stirrer was necessary (4—Fig. 18), as well as sufficient development of the surface of the tube (1—Fig. 18). Of course, by replacing the cryohydrates with pure liquids having correspondingly low freezing temperatures, it would have been possible by the indicated method conveniently to obtain constant temperatures below −65°C. However, for a number of reasons we were unable to verify this experimentally.

The apparatus we used for obtaining lower temperatures is shown in Fig. 19, and the principle of its operation is based on exact observance of equality between the quantities of heat and cold supplied to the thermostat liquid. Liquid air or oxygen from a metal Dewar vessel (1) passed, through an evacuated double-walled glass tube (2), into the cooler (3), from which in the gaseous state, at room temperature, it passed through the rheometer (4). Guided by the readings of the rheometer (4) and the cryostat thermometer, with the aid of the cock (5) such an inflow of liquid air was established as was necessary to maintain a constant temperature in the cryostat under the given throttling regime of the gas under investigation. The Dewar vessel (1) was hermetically closed with a stopper and, through a tube (6) filled with fused caustic sodium and phosphorus anhydride, a purifier (7), and a rheometer (8), was connected with the atmosphere, and through a tube (9)—with a vacuum pump. The cock (10) was opened just enough that a small amount of purified atmospheric air bubbled through the liquid in the vessel (1).

Fig. 19

The arrangement described ensured constancy of the admission of liquid air into the cryostat, independently of its level in the Dewar vessel (1).

In this method, for intensive heat exchange and for creating identical temperatures at all points of the cryostat, intensive stirring of the liquid was also necessary. When working with temperatures down to −80°C, the cryostat was filled with ethyl alcohol, and at lower temperatures down to −150°C—with petroleum ether.

The absolute temperature of the cryostat liquid was measured with mercury, toluene, and pentane thermometers. After the assigned temperature had been established in the cryostat by one of the methods described, the onset of isothermy in the apparatus located in the beaker was concluded only when a mirror galvanometer, alternately connected to the thermoelements \((a)\), \((b)\), \((c)\), \((d)\), \((e)\), \((f)\), gave only slight deviations from the zero position. In all, this usually required 1–2 hours.

To eliminate possible heat losses from the throttle valve by convection, the vessel was strongly evacuated by means of an oil pump (18—Fig. 10) (in our experiments the residual pressure was 0.1–2 mm Hg). In this case, as the experiments showed, some disturbance of the isotherm again occurred. After some time (15–30 minutes) the temperature inside the evacuated vessel again became equalized, after which the gas under investigation was passed through the throttling apparatus at such a rate that the pressure difference, measured by a differential manometer before and after the throttle, was \(\sim 4.5\) atm and, as far as possible, constant. The required absolute pressure and degree of throttling were set by means of valves 6 and 14 (Fig. 10). Simultaneously with the passage of gas into the heating coil of the throttle valve, an electric current was switched on. The strength of the heating current required for exact compensation of the fall in gas temperature was determined as follows. For a certain time the current strength was made somewhat greater than was necessary to compensate the cooling, as a result of which the mirror galvanometer connected to the sensitive compound thermoelement gave deflections in one direction; then the current strength was reduced and the deflections of the mirror galvanometer occurred in the opposite direction. Having thus determined the difference between a slightly greater and a slightly smaller heating current strength, and also knowing the corresponding deflections of the mirror galvanometer when the compound thermoelement was switched on, it was possible, by interpolation, to determine and then set the strength of the compensating current. We note that for a rough preliminary determination of the current strength a milliammeter was used. Only after full compensation of the cooling had been achieved did we proceed to register and record all numerical data needed for calculating the isothermal throttling effect. In doing so, the absolute pressure before and after the throttle was recorded from manometers (10—Fig. 10), the pressure difference was observed from the differential manometer, the cryostat temperature was recorded, and the gas rate was determined from the gas meter, as well as the quantity of electrical energy going to heat the throttle.

The duration of the experiments, after the evacuated vessel together with the throttle valve located inside it had completely assumed the temperature of the cryostat, was \(\sim 1\) hour; the actual operations connected with measurements and recording data after establishment of the isotherm during gas flow took, for one experiment, approximately 15 minutes.

As an example of the recording of experimental data and the subsequent calculations, we give an extract from the laboratory journal.

Extract from the laboratory journal

(Gas being throttled—air)

1. Gas temperature \(273.2^\circ\mathrm{C}\).

2. Absolute gas pressure before throttling \(P_1 = 23.0\ \mathrm{kg/cm^2}\), after throttling \(P_2 = 18.5\ \mathrm{kg/cm^2}\).

Mean absolute throttling pressure:

\[ P_m = \frac{23.0 + 18.5}{2} = 20.75\ \mathrm{kg/cm^2} \]

1. Pressure difference during throttling \(\Delta P\). Distance between the twentieth contacts of the upper and lower mercury-level indicators: \(H_0 = 3411.4\ \mathrm{mm}\).

The upper mercury level was between contacts 7 and 8, and the lower mercury level between contacts 22 and 23; hence the pressure difference \(\Delta P\) in the two limiting cases, corresponding to contacts (7 and 8) and (22 and 23), will be:

\[ \Delta P_{\min}=3411-13.5+2.5=3356\ \text{mm} \]

\[ \Delta P_{\max}=3411-12.5+3.5=3366\ \text{mm} \]

The mean pressure difference:

\[ \Delta P=\frac{3356+3366}{2}=3361\ \text{mm} \]

at a mean temperature of the differential manometer of \(18.9^\circ\text{C}\) (top—19.7, middle—19.0 and bottom—18.0°C),
or \(\Delta P=4.554\ \text{kg}/\text{cm}^2\) (allowing for the correction for the change in the density of mercury with temperature).

1. Gas velocity.

The degree of filling of the gasometer in scale divisions (mm):

The mean filling rate in mm of scale per 1 second is equal to \(0.2553\ \text{mm/sec}\), and 1 mm of scale corresponds in gasometer No. 1 to 0.2177 liter.

The barometric pressure is \(743.5\ \text{mm Hg}\) at \(0^\circ\text{C}\), the pressure in the gasometer is

\[ 743.5+5=748.5\ \text{mm}=0.9849\ \text{atm}, \]

the mean temperature of the gas is

\[ \frac{19.9+19.6+19.5+19.5}{4}=19.62^\circ\text{C}=292.8^\circ\text{K} \]

Gas velocity

\[ V=\frac{0.2553\cdot0.2177\cdot0.09849}{0.08204\cdot292.8} =0.002279\ \text{mol/second}. \]

1. Amount of heat introduced into the throttle valve by the electric current.

According to Table 1, the compensating current strength corresponded to a bridge position of 18.72 divisions.

Table 1

Experimental data required for calculating the heat introduced into the throttle valve by the electric current

The voltage of the 2-volt storage battery, by means of which the voltage drop \(E_i\) was compensated, was equal to 1.881 volts (checked against a standard Weston cell). Thus, the voltage drop across the precision resistance was

\[ E_i=\frac{18.72}{100}\cdot 1.881=0.3521\ \text{volts}. \]

Hence the strength of the heating current is

\[ I=\frac{E_i}{R_{\text{prec.}}}=\frac{0.3521}{9.9986}=0.03522\ \text{amp.} \]

The voltage of the 4-volt storage battery was 3.856 volts. The voltage drop across the heating coil was

\[ E_E=\frac{58.22}{100}\cdot 3.856=2.245\ \text{volts}. \]

The amount of heat liberated by the current is

\[ Q=\frac{E_E\cdot I}{4.1842}=\frac{2.245\cdot 0.03522}{4.1842}=0.01890\ \text{cal/sec}. \]

1. Isothermal throttling effect

\[ \left(\frac{Q}{V}\right)=\frac{0.01890}{0.002279}=8.291\ \text{cal/mol} \]

and, finally, the isothermal throttling effect

\[ \left(\frac{\partial i}{\partial p}\right)_T=\frac{8.291}{4.554}=1.821\ \text{cal/mol and kg/cm}^2 \]

Experimental results

To check the correctness of the operation of the apparatus assembled by us, experiments were carried out to determine the magnitude of the isothermal throttling effect of air. Similar experiments were carried out by Eucken [13]. In addition, the isothermal throttling effect of air can be found from the values of the Joule–Thomson effect, which was determined very accurately by Hausen [6].

We determined the values of the isothermal throttling effect of air at \(0^\circ\mathrm{C}\) and at pressures \(P_m=4.75\) and 20.75 atm.

The results of these measurements are collected in Table 2.

From the given Table 2 it is seen that the numerical values of the isothermal throttling effect of air found by us, in absolute magnitude, at 4.75 and 20.75 atm (temperature \(0^\circ\mathrm{C}\)) are in good agreement both with the determinations of Eucken and co-workers, and especially with the determinations of Hausen. According to Eucken, the isothermal throttling effect at \(0^\circ\mathrm{C}\) and a mean pressure of 4.67 atm is equal to 1.91 cal/mol and kg/cm\(^2\).

Starting from the Joule–Thomson effect determined by Hausen, we calculated the isothermal throttling effect, and at the indicated pressures and temperatures it proved to be equal to 1.877. According to our measurements, the analogous value was 1.880 cal/mol and kg/cm\(^2\).

For a mean pressure of 20.75 atm and a temperature of \(0^\circ\mathrm{C}\), the isothermal throttling effect according to our measurements is equal to 1.822; calculated by us from Hausen’s data, it is 1.83. According to Eucken, the isothermal throttling ...

Table 2

Summary of results for determining the isothermal throttling effect of air.
Temperature \(0^\circ\mathrm{C}\) (water–ice cryostat)

effect even at \(P_m = 28.8\) atm is equal to 1.85, and at a pressure of 20.75 atm this effect should be still greater, since with increasing pressure \(\left(\dfrac{\partial i}{\partial p}\right)_T\) decreases. Calculations from Roubak’s experimental data give a value of \(\left(\dfrac{\partial i}{\partial p}\right)_T\) equal to 1.77.

Of all the indicated data obtained by various authors, the most accurate are Gauzen’s experimental data; our data agree with them.

However, despite the good agreement of our experimental data with those obtained by other authors, nevertheless, at the mean throttling pressure \(P_m = 4.75\) atm and temperature \(0^\circ\mathrm{C}\), we did not obtain complete constancy of the isothermal throttling effect of air. Thus, at the indicated pressure and temperature \(\left(\dfrac{\partial i}{\partial p}\right)_T\), according to our measurements, varies from 1.83 to 1.91, although the majority of experiments for \(\left(\dfrac{\partial i}{\partial p}\right)_T\) give a value within narrower limits.

Such fluctuations of the isothermal throttling effect are explained mainly by the difficulties of creating, at the given low pressure \(=4.75\) atm, a constant gas velocity, as a result of which exact compensation of the cooling becomes difficult. The cause of the indicated difficulty is the insufficient fineness of regulating the gas velocity by means of the Goffe conical valves that we used. To eliminate this shortcoming in subsequent experiments with carbon dioxide

in parallel with the Goffe valve a plunger valve was connected, which made it possible to regulate the gas velocity accurately even at low pressures.

At elevated pressures (in our experiments 20.75 atm) this difficulty, associated with maintaining a constant gas velocity, almost completely disappears, and the isothermal throttling effects observed under these conditions are in good agreement with one another.

For example, experiments 14 and 15 give the value of \(\left(\dfrac{\partial i}{\partial p}\right)_T\), respectively, 1.821 and 1.824.

Eucken and co-workers indicate that in order to obtain correct values of the isothermal throttling effect it is necessary to introduce corrections for the difference in the kinetic energies of the gas before and after the throttle; moreover, these corrections increase as the pressure is lowered, and at a pressure of 4.18 atm and \(t^\circ\) of 269.8° they reach 7%.

The indicated corrections for the kinetic energy of the gas can be calculated from the following equation:

\[ K = A\left(\frac{w_2^2}{2g} - \frac{w_1^2}{2g}\right)M, \]

where \(A\) and \(M\) are, respectively, the mechanical equivalent of heat and the molecular weight of the gas,

\[ \frac{w_1^2}{2g} \quad \text{and} \quad \frac{w_2^2}{2g} \]

are the kinetic energy of 1 kg of gas before throttling and after it.

However, the calculations we performed using the above formula gave a correction that can quite well be neglected. The reason for this is the circumstance that the difference in kinetic energies is strongly influenced by the diameters of the widened parts of the tubes in which the ends of the compound thermoelement are placed. Apparently, the larger corrections found by Eucken and co-workers are explained by the insignificant diameter of the widened part of the tube they used, which carried away the gas after throttling.

In conclusion it may be said that the complex experimental apparatus assembled by us has fully justified itself, since the numerical values of the isothermal throttling effect of air obtained with it are in good agreement with the investigations of other authors. The method makes it possible to investigate accurately the isothermal throttling effect of gases and their mixtures available in relatively small quantities.

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