T H E PRESSURE-VOLUME RELATION HEATED LIQUIDS
OF SUPER-
BY K. .,I WISMER
1.
Introdwetion
The phenomenon of superheating is often observed in the laboratory in the bumping that occurs when a liquid is heated in a clean test tube or beaker. Closely related to this phenomenon is the “mechanical stretching” of liquids which has been investigated by Berthelot, Worthington,2 D i ~ o n , ~ ~ latter having succeeded in subjecting and J. M e ~ e r ,the ether to a stretching, or negative pressure, of 72 atmospheres. But the extent to which liquids can be superheated a t atmospheric pressure has not received much consideration. Conditions corresponding to the minimum point of van der Waals’ P-V curve have been attained by J. Meyer6 in the case of ether, by reducing the pressure on the liquid to zero a t 115”, but he states that he wagnot able to reach zero pressure above 115”. No serious attempts have been made to reduce the pressure of the liquid below the minimum point of van der Waals’ curve. The present research is an attempt to obtain actual P-V curves a t high temperatures t o see whether the curve shows any tendency to bend more sharply as the limit of superheating is approached; to find what degree of superheating may be attained; and, if possible, to discover what initiates the explosion. From the equation (P a / V z )(V - b ) = RT, y obtaining the relation between ‘I’ and V for the condition of the minimum point, and selecting a number of volumes, a projection of the trough of van der Waals’ P-T-V surface on the P-T plane
+
Ann. Chimie, 30, 232 (1850). Phil. Trans., 183, 355 (1892). Proc. Roy. Dublin SOC.,(2) 12, GO (1909-10). “Zur Kenntnis des negativen Druckes in Fliissigkeiten” (1911). Zeit. Elektrochemie, 18, 709 (1912).
302
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K . L. Wisvner
can be drawn. Taking the data for ether, for which most of the measurements were made, a curve was drawn in this way, Fig. 1, Curve 11. The values for the constants a and b were calculated from Ramsay and Young's values for the critical temperature and pressure according to the relationships : 27 TZ Tc b= a= Using T, = 194.4 C., 64 R2P, ' 8 R P,' P,=35.61, and R=0.003764, then a=O.O3668and b=0.006177.
Fig. 1
I Vapour Pressure Curve I1 Minimum-point Curve 111 Lowest Pressures reached experimentally
From this graph it will be noticed that on the basis of van-der Waals' equation, the highest temperature for liquid ether a t one atmosphere pressure is 123". This was remarked by J. Meyer (see above) who, however, by using different values for his constants calculated 115" as the maximum temperature for zero pressure (corresponding to 117' a t 1 atmosphere). 2. Preliminary Experiments Ether, ethyl chloride and isopentane were chosen for study because of their low boiling points and because their critical temperatures and pressures are comparatively low.
Pressure-Volume Relation of Superheated Liquids
303
A few preliminary experiments were carried out to find the highest temperatures to which each of these liquids could be heated at atmospheric pressure ; and to find also the length of time they could be kept under atmospheric pressure a t different temperatures, so that a temperature could be chosen a t which there was a reasonable probability of the liquid holding for a sufficient time to make quantitative measurements. The ether used throughout the experiments was Kahlbaum’s, “iiber Natrium destilliert.” This was again distilled over sodium t o free it from all traces of water, and was kept in a number of small glass-stoppered bottles. Immediately before being used it was boiled to drive out absorbed gases. The ethyl chloride was Hedley’s C. P. “For general anaesthesia.” Sp. Gr . 0.920. The isopentane was Kahlbaum’s, B. P. 29”. Appurutus.-The form of apparatus used is illustrated in Fig. 2. Pressures up t o 50 atmospheres are obtained by
I
Y‘ I
Fig. 2
means of a Fritz Kohler pressure machine, in which a steel rod, S, screws into a cylinder, P, filled with Russian paraffin oil. The pressure is transmitted to the glass part of the
304
K.L. Wisrner
apparatus by a coil of small bore copper tubing. Another coil of copper tubing connects with the pressure gauge D. The liquid under investigation is contained in a capillary U-tube attached at A (not shown in figure). This is separated from the oil in C by a trap of coloured water in the U-tube B. An air-manometer, M, is necessary to indicate atmospheric pressure since the gauge D has a large zero error. E, F and G are tubes used in filling the apparatus with oil, water and the liquid being studied. A tin vessel of 2 liters capacity, covered with two layers of asbestos paper and filled with Russian paraffin oil, served as a thermostat. It was stirred by a motor, and the temperature was kept constant to within l/loo by a gas thermo-regulator. Ether and isopentane were introduced into the capillary U-tube by dipping the turned-down tip into a dish of the liquid, and applying suction at E. Both open tips were then sealed off with a blow-pipe with the liquid as close to the end of the tube as possible, so that the imprisoned gas was for the most part vapour from the liquid, and thus easily compressible to liquid again. To fill with ethyl chloride, which boils at 12.5", the filling-tip E was replaced by a thistle tube into which a few cc. of the liquid were poured and allowed to run down into the capillary by gravity, the tube being kept cold by running tap-water. After breaking off the capillary neck of the thistle tube, the open tips were sealed by touching with the molten end of a glass rod. With every filling the strength of the seal was tested by applying 50 atmospheres pressure. Qualitatiere Results.-Ether was the first liquid investigated. The capillary U-tube was immersed in the thermostat a t 120", under pressure of 20 atmospheres. The pressure was then quickly reduced to 1 atmosphere; the ether exploded in 5 secs., the time being noted with a stop-watch. With this apparatus the same filling of liquid may be used time after time, the formation of vapour in the U-tube merely sending up the mercury column of the manometer until the vapour-pressure is approximately reached, A number of trials were made with increasing temperatures, and it was
Pressure-Volume Relation of Superheated Liquids
305
,
Substance
B. P.
Ether Isopentane Ethyl chloride
35" c. 29 " 12.5"
Highest temp. reached a t 1 atmosphere
143" C. 136" 126"
Press. for min. pt. a t highest temp. *
12.5 atm. 11.0 14.0
Vap. press. a t highest temp.
15.4 atm. 14.3 20.0
* Determined from Curve 11, Fig. 1, and from similar curves for isopentane and ethyl chloride.
306
'
K . L. Wisrner
The highest temperatures reached with ether, isopentane and ethyl chloride, together with the vapour-pressures and the pressures at the minimum points of van der Waals' curve a t these temperatures,are given in Table I. A few experiments were made with ether to determine the lowest pressures that could be reached a t temperatures above 143 O without immediate explosion occurring. The results are shown in Curve 111, Fig. 1. The points are almost on a straight line pointing to the critical point in one direction and very nearly to the -72 atmosphere point of Meyer, a t ordinary temperature. Although the latter must be more or less a fluke, the general position of the points in relation to the vapour-pressure curve (I, Fig. 1) can be accounted for by a simple assumption as to the size of the nuclei which are visible both in liquids and on the glass walls under the ultra-microscope, and round which the initial bubbles may be assumed to form. This, however, is also the subject of another investigation in this laboratory. 3. Quantitative Measurements of Volume The liquids for which P-V curves were obtained were ethyl ether and ethyl chloride. The limited supply of isopentane gave out before a successful result was obtained. Ether was again the first liquid to be investigated quantitatively, and the details of the method will be described for this substance. In making measurements of volume to secure data for a P-V curve, the ether was heated in a thick-walled tube or bulb connected to a fine capillary tube. The obvious method of measuring the volume of the heated ether by separating it from the oil of the pressure machine by a column of mercury, or other insoluble liquid, could not be used because the extent of superheating was much reduced by contact with both mercury and water. After a number of unsuccessful attempts to isolate a quantity of ether by various means and to determine its volume a t atmospheric pressure, the following method was adopted in which the contact point between mercury and ether was ofitside the thermostat: With the contact
Pressure-Volume Relation of Superheated Liquids
307
point a t room temperature, there was no greater probability of an explosion than if the capillary were filled only with ether. Method.-The method can best be explained by an example. A t 133.8' and 20 atmospheres, the heated portion of ether occupies that part of the bulb and tube between c and d , shown diagrammatically in Fig. 3. bc is a length of very fine capillary tube extending out from the thermostat two or three inches, in which there is a temperature gradation from 133.8' a t c to 20 a t b. The end of the mercury thread
1
i
a' a
h
e
\
2
Fig. 3
stands at a,while ab is a section of capillary tube containing ether a t room temperature. When the pressure is reduced to 1 atmosphere, a small amount of ether issues from the bulb, and the mercury stands a t a'. The volume aa', when corrected to the temperature of the thermostat, represents the volume increment for 19 atmospheres. The application of this method involves a number of corrections which will be dealt with later. Apparatus.-Por the quantitative measurements, the pressure machine and manometer were the same as already described. The bulb Y, Fig. 2, is made of heavy glass tubing, about 5 cm. long, with inside and outside diameters of 5 mm. and 8 mm., respectively. This is connected by finebore capillary tubing to a section of fairly uniform tubing, X, of about 1 mm. bore and 2 mm. outside diameter, to which a mm. scale is attached, and into which mercury is introduced for taking readings. This in turn is connected to the U-tube B by a flexible capillary, AN, about one meter long. During the process of "training up" the bulb, the mercury is kept in a side-tube, N, with a layer of water separating it from the ether, which now fills the bulb and the whole length of tube to the water-trap B. In this way a number of explosions
.
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K . L. Wismer
may be allowed to occur without churning up the mercury meniscus, and without allowing ether to touch the mercury and tarnish its surface before the actual readings are made. When the behavior of the bulb indicates a good chance of the explosion holding off long enough to secure a reading at atmospheric pressure, the temperature of the bulb is raised about 10" while the pressure is kept a t 25 atmospheres, and the side-tube N is pulled forward and upwards (the flexibility and torsion of the capillary line allows this), until the mercury runs down into the befld of the tube, and closes off a portion of ether in the tube and bulb. On cooling the bulb again t o the temperature of the thermostat, the.mercury is drawn up into the capillary X in readiness for readings. Starting with, say, 50 atmospheres, the position of the mercury column is noted at intervals of 5 atmospheres. One or two explosions after the introduction of the mercury usually rendered the apparatus unfit for further use, and the tubes and bulbs had to be remade and refilled. It may be mentioned that while no bulbs ever burst during the experiments, a bulb purposely broken in the thermostat scattered the oil for about 6 feet in all directions, and badly distorted the tin vessel. As a protection to the experimenter, the thermostats were housed in a case of wire-reinforced plate glass, with a slot a t the side through which the bulbs could be manipulated. Measurements and Corrections.-At the conclusion of a set of readings, the volume of the bulb (c t o d, Fig. 3) was calculated from the weight of mercury filling it when at the temperature of the bath, and thus the correction for the thermal expansion of the glass becomes unnecessary. The tube X in which readings were taken was calibrated by means of a thread of mercury. Employing the foregoing method, corrections must be made for: (1) Enlargement of bulb due to pressure: The bulb and part of the graduated stem were filled with mercury, and placed in the thermostat, The apparent compression, less the known
Pressure-Volume Relation of Superheated Liquids
309
compression of mercury, gave the expansion of the glass due t o pressure. This correction, at most, amounts to 0.07%. (2) E x p a n s i o n of volume ab on reducing pressure: This portion of ether was a t room temperature, and the correction was easily made from Amagat's compressibility coefficients. It is at most 0.0570 of the total volume, and therefore practically negligible. (3) Temperature correction for volume aa': Since no thermal expansion data were available for the high temperature and low pressure conditions of this research, use was made of the values for the volume of one gram of ether at high temperatures and the corresponding vapour-pressures determined by S. Young.* For ethyl chloride a special experiment was made at the vapour-pressure, Thus at only one pressure does the correction hold strictly true, the corrected values of the volume aa' being slightly too large for pressures above the vapour-pressure, and slightly too small below the vapour-pressure. (4) Temperature change on adiabatic expansion: This correction is required only in the last pressure reductions where the liquid is in an unstable state and there is no time to wait for temperature equalization between bulb and bath. To determine the temperature change on adiabatic expansion: a long thin-walled glass bulb with fine capillary to serve as an air-thermometer was sealed into a larger bulb which was attached to the pressure machine and filled with ether. A short thread of oil was inserted in the thermometer capillary to register temperature changes. A rise or fall in pressure of 20 atmospheres gave a sharp displacement of the oil of 2 mm., which slowly returned t o its original position after 50 secs. This displacement corresponded to a temperature change of 0.G". This value, along with the thermal expansion coefficient of ether, calculated from Young's data (see above), were used to make the adiabatic volume correction. Unfortunately conditions have not permitted a similar deterAnn. Chim. Phys., 11, 530 (1877); 29, 505 (1893). Proc. Roy. Dublin SOC., (2) 12, 374 (1909-10).
K . L. Wisnzer
310
mination for ethyl chloride, and consequently only those rneasurements could be made for which there was sufficient time to allow temperature equalization to take place. Applying these corrections, if T = temperature of the thermostat, and P ~ = o n eof a succession of pressures, the volume a t a temperature, T, and a pressure, PI, becomes: V (expansion of glass bulb for PI atms.) (vol. aa') (1 aXotoTAT)- (VOI. ab) P,, A P V ~ TDT, O where V=vol. of bulb a t temp. T and atmospheric pressure. AT= T -room temperature. A P = Po- Pi. Pa=initial pressure. DT =adiabatic temp. change. cy=coeff. of thermal expansion of the liquid. P = coeff. of compressibility of the liquid. For example, at 133.8" and 48.4 atms., the vol. of ether = 0.96299 0.00067 . . . . . . . . . . . . . . . . . . . . . .0.96366 cc. At 133.8" and 19.3 atms., volume=0.96299 0.00035 0.02085 (1 0.00261 X 114) - 0.0448 X 176 X 29.1 = 0.99014 cc. At 133.8" and 1 atm., volume= 0.96299 0.03493(1 0.00261 X 114)-0.0448 X 176 X X 47.4 0.96299 X 0.00356 X 0.6 = 1.00997CC. In addition to the above easily made corrections, the following are more difficult to take into account, but their omission does not appreciably affect the accuracy : (1) cr is probably not independent of pressure in correction (3) above. Since the total correction amounts to only about 1% of the volume of the liquid, a slight error in the value of a! will obviously be negligible. A rapid turning of the lower end of the 133.8' curve for ether might cause a considerable change in cy, but the plotted results show that this is not the case, and there is therefore no appreciable error in the use of cy determined a t the vapour-pressure. (2) The volume bc, in which there is a temperature gradation from the temperature of the thermostat to room
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Pressure-Volume Relation of Su9erheated Liquids
311
temperature, is not more than the volume of ab, and a compressibility correction is therefore unnecessary. (3) There is a lag in the flow of liquid through the capillary bc. This introduces the largest source of error, but affects only the last readings in the experiments with ether. All that can be said is that there is a possible maximum error of about 7% in the last volume increment, or 0.3% on the whole volume.
Fig, 4
Fig. 5
Results.-The results ."for ether a t 121.5", 127.9' and 133.8", and for ethyl chloride-at 99.6', 109.7' and 117.4' C. are given in Tables I1 and 111. In the columns under the head of "time" are given the times in seconds which were allowed after each pressure reduction before taking the reading. The volumes, with all the corrections applied (Column VI) were converted to the basis of the volumes of 1 gram (Column
VII)* and are represented graphically in Figures 4 and 5. These curves show no unusual tendency to curve sharply in the low pressure regions, although the 1 atmosphere point on the ether curve at 133.8" is 7l/2 atmospheres below van der Waals' minimum point, and 13 atmospheres below the vapour-pressure. The very great divergence of actual pressurevolume relations from van der Waals' theoretical curve is very strikingly shown in Fig. 6, in which the unit of volume
TABLE11-Ether I Press. atms.
I
I1 Temp. den. C
17.9 15.5 13.5 11.6 9.7 1.0
121.5 121.5 121.5 121.5 121.5 121. ti
48.4 44.5 38.7 34.8 29.0 25.2 19.3 15.5 11.6
127.9 127.9 127.9 127.9 127.9 127.9 127.9 127.9 127.9 127.9
1.0 48.4 43.5 38.7 33.9 29.0 24.2 19.3 1.0
I11 Time secs.
-
-
I
10
-
-
-
30 133. 8 30 133.8 30 133.7 30 133.7 30 133.7 30 133.7 133.7 30 133.8 loment
IV Scale reading
V Vol. aa' incorrectec
VI Volume in cc.
v11 Volume of 1 g.
10
31 47 73 228
0 0.00250 0.00443 0.00688 0.00957 0.02184
1.59421 1.59671 1.59864 1.60089 1.60378 1.61605
1.7334 1.7368 1.7394 1.7424 1.7464 1.7630 '
35.5 42 63.5 82 118 142 192 233 287 386
0 0.00343 0.00957 0.01322 0.01992 0.02435 0.03176 0.03653 0.04147 0.05473
1.66574 1.67008 1.67780 1.68238 1.69080 1.69637 1.70568 1.71.168 1.71789 1.73597
1.7267 1.7312 1.7392 1.7440 1.7527 1.7585 1.7681 1* 7743 1.7808 1.7995
-3 6.5 20 41 72 107 157 296
0 0 .'00310 0.00600 0.00934 0.01310 0.016jO 0.02085 0.03493
0.96366 0.96759 0.97126 0.97550 0.98029 0.98461 0.99014 1.00997
1.7550 1.7622 1.7689 1.7766 1.7853 1.7932 1.8033 1,8394
SO
* For ether the conversion was made with S. Young's data at the vapourpressure. In the case of ethyl chloride the conversion is dependent on the special experiment referred to on page 309, which was not done accurately. The numbers in Col. VII, Table 111, may therefore have a constant error of as much as 1% throughout.
Pressure- Volume Relation of Superheated Liquids
--
’
TABLEIII--Ethyl
3 13
chloride VI I Jolume* of 1 g.
I Press. atms.
I1 Temp. deg. C.
I11 Time secs.
IV Scale readings
V Vol. aa’ ncorrec ted
VI Volume in cc.
48.4 43.5 38.7 33.9 29.0 24.2 19.3 14.5 9.7 8.0 4.0 2.0 1.0
99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6 99.6
-
15 15 30
174 181 187.5 195 203 210 218 225 233 235.5 34 1 244 215
0.0 0.00101 0.00198 0.00310 0.00432 0.00540 0.00662 0.00778 0.00908 0.00950 0.01042 0.01095 0.01110
3.51757 1.2426 3.51861 1.2451 3.51963 1.2475 3.52078 1,2503 3.5220.5 1.2533 3,52318 1.2561 0.52445 1.2591 0.52566 1.2620 0.52703 1.2653 0.52757 1.2664 0.52844 1.2687 0.52898 1.2700 0.52913 1.2703
48.4 43.5 38.7 33.9 29.0 24.2 19.3 14.5 9.7 8.0 4.0 2.0 1.0
109.7 109.7 109.7 109.7 109.7 109.7 109.7 109.7 109.7 109.7 109.7 109.7 109.7
30 30 30 30 30 30 30 30 30 45 45 45 50
241 248.5 255.5 263 270.5 278 286 293 300.5 305 31 1 314 335.5
0.0 0.00123 0.00245 0.00375 0.00512 0.00640 0.00794 0.00920 0.01066 0.01155 0.01273 0.01331 0.01362
0.51757 0.51887 0.52018 0.52156 0.52303 0.52440 0.52609 0.52741 0.52898 0.52997 0.53125 0.53185 0.53219
1.2688 1.2720 1,2752 1.2786 1.2822 1.2856 1.2897 1.2930 1.2967 1.2992 1.3024. 1.3038 1.3046
48.4 43.5 38.7 33.9 29.0 24.2 19.3 14.5 9.7 8.0 4.0 2.0
117.3 117.35 117.35 117.35 117.4 117.5 117.5 117.45 117.45 117.45 117.5 117.5
90 40 40 40 40 40 40 40 40 20 20 10
290 297.5 304.3 312 320.5 328 336 343 350.5 354 358.3 360.5
0.0 0.51757 0.00138 0.51909 0.00268 0.52052 0.00420 0.52225 0 00590 0.52409 0.00740 0.52577 0.00906 0.52761 0 . 01060 0.52932 0.01225 0.53115 0.01302 0.53224 0.01397 0.53349 0.01445 0.53442
1.2941 1.2978 1.3014 1.3058 1.3103 1.3145 1.3192 1,3234 1.3280 1.3307 1.3338 1.3362
* See
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-
footnote, page 312.
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K . L. Wismer
in van der Waals' curve is so chosen that it corresponds with the actual volume of 1 gram of liquid ether a t 50 atmospheres. The high degree of superheating, and the great uncertainty of explosions, imposed unusual conditions on the experiments, and the occurrence of a. great many failures explains the restriction of the investigation to two liquids.
Fig. 6
4.
Summary
(1) The highest temperatures of superheating a t atmospheric pressure were : ethyl ether, 143'; isopentane, 136 O ; ethyl chloride, 126 '. (2) The minimum pressures which can be reached with liquid ether a t temperatures above 143" increase with the temperature, the points lying approximately on a straight line joining the critical point with the -72 atmospheres point ,of J. Meyer. (3) The pressure-volume relation was determined experimentally for liquid ethyl ether a t 121.5", 127.9' and 133.8', and for liquid ethyl chloride at 99.6", 109.7' and 117.4' a t pressures down to 1 atmosphere.
Pressure-Volume Relation of SuQerheated Liquids
315
(4) The pressure-volume relation under these conditions was almost linear. There was. no tendency shown by the P-V curves to bend more sharply a t low pressures as the limit of superheating was approached. Actual experiments showed a marked departure from van der Waals’ curve. This research was carried out a t the suggestion and under the direction of Prof. F. B. Kenrick. University of Toronto Department of Chemistry June, 1921
