Bridgman’s Investigations in the Field of High Pressures.

Privatdozent A. V. Rakovsky.

PART II.

PROPERTIES OF LIQUIDS.

The first experiments concerning the thermodynamic properties of liquid mercury were carried out by Bridgman in apparatus with a movable ring, constructed after the type of those instruments in which he studied the compression of solid bodies. However, this method, accurate for solid bodies, proved insufficiently accurate for liquids, in view of the inevitable leakage of the liquid along the piston. Bridgman therefore turned to the piezometric method. He constructed a series of steel piezometers, without even attempting to work with glass piezometers. The point is that already from the work of Amagat, de Metz, Richards, and others it could be concluded that glass piezometers introduce a large individual error. In Bridgman’s investigations devoted to the electrical resistance of mercury under various pressures, it was found, besides the extraordinary fragility of glass under high pressure, that under the influence of pressure not only the volume of a glass vessel changes, but also its shape. The change in the shape of the vessel, owing to the inhomogeneity of the glass, differs in different vessels, and this fact introduces an individual error for each vessel, differing from vessel to vessel and not susceptible to accounting. Further, for some particular cases, as, for example, for liquid mercury, the change in the volume of the glass vessel constitutes too large a percentage of the change in the volume of the mercury itself. The correction turns out to be very large, and consequently unreliable.

After it had turned out that steel does not amalgamate if it is under all-round pressure, Bridgman was able to begin work in steel piezometers.

Figure 1 shows the construction of such a piezometer. In the cover \(B\) there is a channel \(E\), tightly stopped with a bolt, along which a scratch has been made. Through this scratch mercury can pass, but the scratch—

the curvature is so small that the protruding droplet of mercury is scarcely noticeable and, on ordinary scales, is weightless. The piezometer is used in the upright and inverted positions. In the upright position the vessel is filled with water, the lid is screwed on, mercury is poured into the recess, and the piezometer is inserted into the pressure chamber. When the pressure is increased, the water diminishes its volume and the mercury penetrates into the vessel, where it falls to the bottom. After removal of the pressure and opening of the piezometer, the weight of the mercury that has penetrated inside is determined; from the weight of the latter the change in volume is determined, after making, of course, all the necessary corrections for deformation of the steel piezometer, temperature, etc.

Fig. 1.

In the case of using the piezometer in the inverted position, the piezometer is filled with mercury and water, and the pressure chamber with water. In the inverted piezometer the mercury will take its place at the lid and, consequently, will cover the channel. When the pressure is increased, the water will enter the piezometer and float on top of the mercury. When the pressure is removed, the contents of the piezometer expand, whereby the mercury is forced out. From the weight of the expelled mercury one can calculate the magnitude of the compression of the liquids in the piezometer.

In the method described, two liquids are studied simultaneously, in particular mercury and water1. The changes in the volume of the piezometer are determined from the coefficient of compression of steel. To compute the changes in volume $\Delta v$ of water and mercury, one must resort to the method of successive substitutions2.

The dependence of the volume $V$ of liquid mercury on the pressure $p$ was studied at $0^\circ$ and $22^\circ$. To obtain the value of $p$ and $v$, Bridgman carried out experiments at $0^\circ$ in 5 piezometers and obtained about 90 figures; for the temperature $22^\circ$ he obtained 38 points with the 2 best piezometers. The experiment showed that steel piezometers also introduce—though, to be sure, insignificant in comparison with glass ones—an individual error, i.e., at high pressures they slightly change their shape. The magnitude

of this error probably depends on the degree of uniformity of the hardening of the steel. Plotting the curves \((p, v)\) from the data of various piezometers, we can easily distinguish the better piezometers from the worse ones and, accordingly, assign different weights to the series of figures when processing the material. The processing itself of the numerical material is very interesting, but we cannot dwell on it here.

The piezometric method, quite satisfactory in itself, suffers, however, from the disadvantage that it requires much time and labor from the experimenter, since obtaining each number requires assembling and disassembling the entire apparatus (the pressure chamber and the piezometer). After Bridgman succeeded in constructing cylinders with pistons without the slightest leakage of liquids along the piston, he abandoned the piezometric method and turned to the “piston” method.

For studying the thermodynamic properties of liquids (the experimental determination of the values of the volumes of liquids at various temperatures from \(0^\circ\) to \(80^\circ\) and at pressures from 1 to 12500 kg/cm\(^2\)), Bridgman in his later works uses one cylinder, in the internal cavity (the pressure chamber) of which there are placed: at the bottom—a manganin manometer; in the middle—a steel vessel (a small bomb) with the liquid under investigation; and in the upper part—a piston that does not allow leakage. The entire pressure chamber is filled with gasoline. The piston, forced inward by a hydraulic press, is provided with a micro-screw permitting the motions of the piston to be recorded with an accuracy of up to \(0.0001''\). Knowing the cross-section of the piston and its travel, one can accurately calculate the changes in the volume of the internal cavity of the cylinder, after introducing, of course, corrections for the elastic deformation of the cylinder and piston under the influence of changes in pressure and temperature. The whole apparatus is, of course, placed in a thermostat.

Fig. 2.

In the case of water (which was introduced into the pressure chamber in a small bomb), the gasoline either pressed directly on the water, or the water was separated from the gasoline by a column of mercury. Parallel experiments showed that, under direct pressure of gasoline on water, the latter does not change its properties.

Figure 2 shows the arrangement of the instruments in the pressure chamber in the case of organic liquids. The liquid under investigation is introduced into the steel vessel \(A\), the lower part of which is immersed in the recess \(B\), filled with mercury. The lower cutout \(B\) closes the manganin manometer, which fits onto the projection \(C\), screwed into the bottom of the chamber.

In the “piston” method the experiments are conducted in two ways. One may, at constant temperature, vary the volume of the system and determine the pressure corresponding to a given volume; or else, keeping the piston immobile, vary the temperature and seek the pressure as a function of temperature: in the latter case we obtain \(\left(\dfrac{\Delta p}{\Delta t}\right)_v\), and then compute \(\left(\dfrac{\Delta v}{\Delta t}\right)_p\) by the generally known formula of thermodynamics.

For water, by this method Bridgman carried out 18 series of experiments; for 12 other liquids, for each on the average, 140 points were obtained (75 for compressibility and 65 for thermal expansion). For each point there are 2 pressure readings and 4 piston readings. In all, 12,500 readings were made. Despite the enormous mass of figures, only 4 months of work were spent on the principal series of experiments with 12 liquids (not counting, of course, the time for preliminary experiments).

In the piston method the piston takes account of changes in the volume of the entire pressure chamber. In order not to introduce a series of corrections for the compression or expansion of all the substances in the chamber (gasoline, steel, manganin wire, etc.), Bridgman always made, under otherwise equal conditions, two experiments: one with the liquid, the other in which the steel vessel with the liquid was replaced by a solid piece of steel of the same volume, with known coefficients of compression and thermal expansion. The difference in the readings of such two experiments is equal to the difference between the property (for example, the compressibility) of water and that of steel1. The compressibility and thermal expansion of steel are known (0.00000058 and 0.000039).

The numerical material obtained by Bridgman for mercury, water, and 12 other liquids is extremely abundant. From the experimental data for volume, pressure, temperature, and, in many cases, the compressibility and thermal expansion of the liquids, Bridgman, for each liquid, calculated by known thermodynamic formulas a whole series of derived functions, such as the mechanical work in compression, the heat evolved in isothermal and adiabatic compression, changes in internal energy, heat capacities, etc.

It should be noted that the investigations carried out with water and mercury apparently give rise to no doubts; as for the other liquids, here Bridgman committed a small carelessness, characteristic of physicists of the good old days, namely:

he was compelled to investigate commercial preparations and only 9 months after completing his work to submit these liquids to the chemical laboratory. Fortunately, most of the preparations proved either quite good (alcohols, ether, carbon disulfide), or satisfactory; two preparations, however, phosphorus trichloride and acetone, proved to be entirely impure substances, since \(PCl_3\) boils in the range \(77^\circ\)—\(102^\circ\), acetone in the range \(56^\circ\)—\(59^\circ\). However, in view of the fact that most of the liquids were satisfactory, and that Bridgman studied their properties at pressures of 2000 and more kg/sq. cm., where the influence of impurities in small quantities is negligible, this work of Bridgman retains its full scientific value, losing only in the elegance so characteristic of all the other works of this talented investigator.

Turning now to the exposition of the results of Bridgman’s investigations, I shall dwell only on the most important of them, those of general interest, referring the reader for details to Bridgman’s original articles.

The volumes of liquids with change of pressure can vary, of course, in only one direction, namely, decrease with increasing pressure. Much more complex is the change of volume with temperature (at constant pressures). For a normal liquid the general form of the curve \((v,p)_t\) ¹—the isotherm—and the curve \((v,t)_p\)—the isochore—is represented in Figure 3. But already for water we know that its curve \((v,t)_p\) passes through a minimum at \(4^\circ\) (the maximum density of water). If we draw a series of curves \((v,p)_t\) for different temperatures, then for water we obtain a bundle of curves, crowded together at the beginning and diverging at medium pressures. For other liquids there is no crowding of these curves at low pressures.

Fig. 3.

In connection with the indicated abnormality of water at low pressures stand abnormalities in a number of other properties of water, and the most probable explanation of such behavior of water lies in the association of the molecules of liquid water. For simplicity we assume that the molecules of water in liquid water may be simple \(H_2O\) and double-

¹ The expression “the curve \((v,p)_t\)” denotes the curve showing the dependence of volume on pressure at constant temperature.

... \((H_2O)_2\). A double molecule must occupy a larger volume than the volume of two simple molecules. When the temperature of water falls, there occurs the natural decrease in volume characteristic of every normal substance (a decrease in the distances between molecules), but at the same time the degree of association of the molecules increases, i.e., the volume of the water increases. At \(4^\circ\) this increase neutralizes the natural decrease in volume, and at lower temperatures it predominates; consequently, the volume of water increases as the temperature falls below \(4^\circ\). At very low temperatures, when almost all the molecules in the water are already double, a further lowering of the temperature must again cause a decrease in volume. Consequently, the complete curve \((v,t)_p\) must have the form shown in Figure 4. At high temperatures there are few double molecules, and therefore water must behave normally.

Fig. 4.

The reproduction of the complete curve (Figure 4) in experiment was not achieved by Bridgman, because it is difficult to supercool water below \(-10^\circ\) at low pressures. But since Amagat had already observed, at elevated pressures, not a diminution of the minimum of the water curve \((v,t)\), but only a displacement of it toward lower temperatures, and since at higher pressures water can be kept in the liquid state even below \(-20^\circ\), Bridgman studied in detail the curves \((v,t)_p\), at intervals of every \(500\ \mathrm{kg}/\mathrm{sq.\ cm}\). The curves obtained by him are shown in Figure 5. It turned out that at \(1500\ \mathrm{kg}/\mathrm{sq.\ cm}\) the real curve fully reproduces the theoretical curve of Figure 4. At \(2000\ \mathrm{kg}/\mathrm{sq.\ cm}\) only traces of this abnormality are observed; it is no longer present at \(2500\ \mathrm{kg}/\mathrm{sq.\ cm}\) and above. But an abnormality of the same kind apparently appears in water again at a pressure of \(5000\ \mathrm{kg}/\mathrm{sq.\ cm}\). If a perfectly legitimate small extrapolation of the experimental curves is made, it will turn out that water at \(5000\ \mathrm{kg}/\mathrm{sq.\ cm}\) must expand in passing from \(-15^\circ\) to \(-20^\circ\). Here we are in the region of pressures and temperatures where ices V and VI appear.

Fig. 5.

In any theory of liquids, the volume of the molecules themselves plays a large role. Tumlirz and Tammann, proceeding from their theories, calculated

volume of the liquid at infinitely great pressure. Bridgman compares their calculated values with those found at 12000 kg/cm² (20°). The volume of the given liquid at ordinary pressure is taken as unity.

TABLE I.

In the fact that the volume of ether at 12000 kg/cm² is less than the calculated limiting volume of the molecules, one cannot, of course, see evidence in favor of the compressibility of molecules, since theories of liquids at the present time are still very unreliable.

On considering the volumes of liquids over wide ranges of pressure, it turned out that one cannot ascribe a definite volume to atoms and calculate, according to the law of additivity, the volume of a chemical compound in the liquid state. Thus, the volumes of ether ($C_2H_5OC_2H_5 = C_4H_{10}O$) and of its isomer, isobutyl alcohol ($CH_3CH_2CH(OH)CH_3 = C_4H_{10}O$), at atmospheric pressure are related to one another as 1.102, and at 12000 kg/cm² as 1.038.

It is interesting that the form of the curves $(p, v)_t$ for many liquids (11) is one and the same. The curve, where on the ordinate axis $\Delta v$ is laid off (changes in volume at each 500 kg/cm²), and on the abscissa axis—the pressure $p$, can be represented by the equation:

$$ \Delta v = \alpha P^{0.8} + \beta P^{0.6} + \gamma P^{0.4} + \delta P^{0.2}, $$

where

$$ P=\frac{p-500}{1000}. $$

In passing from one liquid to another, it is sufficient to multiply all the constants of this equation by one and the same factor²).

¹) All liquids, with the exception of mercury, decrease their volume at 12000 kg/cm² approximately to 3/4 of the volume at atmospheric pressure. The volume of mercury at 12000 kg/cm² and 22° falls to 0.966.

²) Bridgman calculated the mean values of the constants for 11 liquids: $\alpha=-0.0029$, $\beta=-0.0546$, $\gamma=+0.2969$, $\delta=-0.1804$. In order to pass from this mean equation to the equation, for example, for ether, all constants must be …

Clearer differences between liquids appear in their properties that are derivatives of volume, such as compressibility, thermal expansion, heat capacity, etc. We shall dwell briefly on some of these properties of liquids.

Compressibility — \(\left(\dfrac{\partial v}{\partial p}\right)_t\). From the kinetic point of view, compressibility should decrease with increasing pressure and, at higher temperatures, should be greater than at lower ones. Figure 6 shows curves of the variation of compressibility with pressure at \(0^\circ\) and \(22^\circ\) for mercury, and Figure 7 for water. Compressibility, as was to be expected, in both cases decreases with increasing pressure, but according to different laws: for mercury the curves are turned toward the axis of abscissas with their concavity, for water—with their convexity. For mercury the compressibility at higher temperatures is greater than at lower ones; water behaves anomalously in this respect. At low pressures the compressibility decreases with increasing temperature up to \(50^\circ\); at temperatures above \(50^\circ\) the compressibility increases, but even at \(80^\circ\) its value is less than at \(0^\circ\)\(^{1}\).

Fig. 6.

The form of the curves for other liquids is the same as for water, but, in general, compressibility increases with increasing temperature. Above 4000 kg/sq. cm the corresponding curves come very close together.

Fig. 7.

multiply by the factor 1.104; ether is the most compressible substance. The factor for acetone is 1.049, for ethyl alcohol 0.9979, etc., for propyl alcohol 0.8726 (the least compressible substance among those studied by Bridgman). Ethyl chloride did not fit this formula; for it the constants are essentially different: \(\alpha = 0.06723\), \(\beta = 0.17139\), \(\gamma = 0.0403\), \(\delta = -0.06261\).

\(^{1}\) The curve \(\left[\left(\dfrac{\partial v}{\partial p}\right)_{80^\circ}\cdot p\right]\) lies between the curves of Fig. 7. Above 4000 kg/sq. cm.

and here small anomalies are observed, at times lying within limits very close to the errors of experiment.

External pressure \(p\) is considered an unfortunate variable because it is in some dependence on the internal pressure and on the properties of the surface layer of the liquid. A variable independent of the surface layer is the volume \(v\). If one constructs the curves

\[ \left[\left(\frac{\partial v}{\partial p}\right)_t,\, v\right], \]

then one obtains curves of the same type as in Figure 7, but for water the anomalies disappear: at one and the same volume the compressibility is always smaller at higher temperatures than at lower ones. This phenomenon should also be expected from the kinetic point of view. At one and the same volume, at higher temperatures the molecules move more rapidly and create greater resistance to pressure than at lower temperatures; consequently, the compressibility must be smaller.

The same curves

\[ \left[\left(\frac{\partial v}{\partial p}\right)_t,\, v\right] \]

are obtained for other liquids, with the exception of carbon disulfide and ethyl chloride.

If, for ease of survey, we consider the compressibility \(K\) of liquids, averaged over \(20^\circ\)—\(80^\circ\), at various pressures, we obtain the following table.

TABLE II.

cm, the curves intersect, the phenomena become reversed, but even at 6500 kg/sq. cm a small anomaly is observed near the melting point of ice VI.

Using the table, find:

TABLE III.

Thermal expansion, $\delta=\left(\dfrac{\partial v}{\partial t}\right)_p$, Bridgman computed either as the mean between two temperatures, or as $\delta$ at a given temperature. The methods of calculation are very interesting, but also complex, and therefore we shall not dwell on them here. In view of the comparatively limited temperature interval, the effect of pressure on $\delta$ was studied in detail, and curves

$$ \left[\left(\frac{\partial v}{\partial t}\right)_p,\ p\right] $$

were constructed. Such curves are shown for mercury in Figure 8, and for water in Figure 9. Water approaches the mercury type only at high temperatures, $60^\circ$ and $80^\circ$. At $0^\circ$ $\delta$ increases with pressure and, as Amagat predicted, at 4000 kg/sq. cm passes through a maximum. The curves for $20^\circ$ and $40^\circ$ are of interest. It is hardly possible here to admit experimental error: four independent series of experiments gave one and the same curve. Other liquids for the most part give normal curves; only for carbon disulfide, acetone, and ethyl iodide has an increase $(\delta_{20})$ with pressure been found. On the other hand, the relations between the curves $(\delta_t,p)$ for one and the same liquid, but for different $t^\circ$, are very peculiar. As a rule, the curves for different temperatures $(20^\circ—80^\circ)$ intersect at one point $A$ (Figure 10), where

$$ \frac{\partial^2 v}{\partial t^2} $$

changes sign, and does not become zero, as Tamm assumes in his theory.

Fig. 8.

Fig. 9.

In the region below \(A\), at higher \(p\), interlacings of the curves are observed, and sometimes all the curves intersect at one point, i.e.

Fig. 10.

there occurs a new change of sign of \(\frac{\partial^2 v}{\partial t^2}\). Figure 11 shows such curves for ethyl alcohol.

Fig. 11.

The complexity of the relations among \(\delta_t\) for ethyl alcohol is seen still more clearly from the following table.

TABLE.

The curves of the mean thermal expansions between \(20^\circ\) and \(80^\circ\) are simpler. As for the absolute values \(\delta_{20^\circ-80^\circ}\), Table 4 gives some idea of them.

TABLE IV.

The coefficient of increase of pressure with temperature at constant volume,

\[ \gamma=\left(\frac{\partial p}{\partial t}\right)_{v}, \]

shows the change in pressure when the temperature of the liquid at constant volume is raised by \(1^\circ\). According to Ramsay and Shields, this coefficient is a function only of the volume, and, consequently, the curves expressing the relation between volume and \(\gamma\) for different \(t^\circ\) and \(p\) should coincide. According to Amagat’s data, up to \(3000\) kg/sq. cm this phenomenon does indeed occur (the deviations of the curves are very small), but when the range of pressure is extended to \(12500\) kg/sq. cm, not a single liquid gave coincidence of these curves.

The change of internal energy \(\Delta E\) of a liquid under isothermal compression is equal to the difference between the heat of compression and the work of compression1. When molecules are brought closer together under the influence of pressure, attractive forces act, owing to which the internal energy of the liquid decreases. If this energy of the liquid is smaller at higher pressures than at lower ones, this means that the work of the attractive forces between the molecules is greater than the mechanical work of compression. At very high pressures one may expect compression of the molecules themselves and, consequently, not a decrease but an increase of their potential energy. From this point onward one should expect an increase in the internal energy of the liquid. In the general case, therefore, the internal energy of a liquid, with increasing pressure, must pass through a minimum.

For water the internal energy falls up to \(12500\) kg/sq. cm; only at \(0^\circ\) is there an indication that this energy passes through a minimum; the same has been found for mercury, methyl alcohol, and propyl alcohol. The internal energy of all the remaining liquids, with increasing pressure, passes through a minimum. A more detailed consideration of the dependence of this energy on volume leads Bridgman to the conclusion that at higher pressures the molecules of the liquid come into direct contact and change their shape.

The heat capacity at constant volume \(C_v\) is the most interesting of the other thermodynamic properties of liquids considered by Bridgman. It is usually assumed that \(C_v\) contains only the energy necessary to raise the temperature of a substance, and that this rise in temperature consists in an increase of the kinetic energy of the molecules (in a gas) and of the atoms (in solids—the law of Dulong and Petit). The heat capacity \(C_v\) should not depend on pressure or temperature. Indeed, for mercury up to 7000 kg/sq. cm only a very small increase of \(C_v\) is observed.

\[ \begin{aligned} \text{At } \quad &1 \text{ kg/sq. cm} \quad \ldots\ldots\ldots\quad C_v=0.0294,\\ &7000 \quad "\quad "\quad "\quad \ldots\ldots\ldots\quad C_v=0.0300. \end{aligned} \]

For all the other liquids, complicated relations have been found for \(C_v\) at different pressures and temperatures. The dominant phenomenon is an initial decrease of the heat capacity with increasing pressure, then an increase (the curve \(C_v\) passes through a minimum). In general, the same picture is observed both for the curves \((C_v, v)\) and for the curves \((C_v, p)\).

The initial decrease of the heat capacity with increasing pressure may perhaps be explained by phenomena of association of molecules. When simple molecules, under the influence of pressure (at constant temperature), pass into double ones, the number of molecules in 1 gram of substance decreases, in the limit to one half, and the heat capacity \(C_v\) also decreases. As for the increase of heat capacity at high pressures, Bridgman considers this fact an indication of the appearance of an ordered arrangement of molecules; moreover, at high pressures, when the molecules are partly in contact, temperature becomes a molecular atomic function.

In connection with the question of the essence of temperature in liquids stands the question of the kinetic nature of pressure. It is evident that at high pressures, when the molecules of a liquid have no free space for their motions at all, the pressure produced by the liquid on the walls of the vessel cannot be explained by changes in the momentum of molecules striking the wall. In this case the molecules act like compressed springs. Proceeding from such considerations, Bridgman sketches the outlines of a theory of the liquid and derives a new equation of state, in which there is a coefficient taking account of the elasticity of the molecular spring. We shall not dwell on this theory, since it is only sketched, and its development will probably be the subject of Bridgman’s further work.

(The conclusion follows).

1. The heat of compression \(Q=\int T\left(\frac{\partial v}{\partial t}\right)_{p}\,dt\), the work of compression \(W=\int p\left(\frac{\partial v}{\partial p}\right)_{t}\,dp\). ↩↩↩

2. First the calculation of $\Delta v$ is carried out for water under the assumption that the coefficient of compression of mercury does not depend on pressure and is equal to the coefficient of compression at ordinary pressure. Then $\Delta v$ is calculated for mercury, using the just obtained changes of the volume of water with pressure. The data obtained for mercury are applied to a second series of computations of $\Delta v$ for water, which are again applied to the next series of computations of $\Delta v$ for mercury, and so on. For mercury and water in Bridgman’s experiments, two series of computations for each liquid proved sufficient. ↩