58
THE JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
especially in the case of oils with a low acid content. Alcoholbenzene mixture gives values which are correct within the limits of experimental accuracy of the determination. With rosin-tung oil mixtures, alcohol-benzene gives results nearer the theoretical than does alcohol alone. 2-Alcohol as a solvent in the determination of the acid number of linseed and cottonseed oils yields values which average slightly lower than the theoretical acid content. I n most of the determinations the average of the values obtained with alcohol-benzene mixture were closer to the theoretical acid content than when alcohol was used as solvent. 3-Alcohol-benzene mixture is preferable to alcohol as a solvent because the end-point in the titration is much sharper. 4-As was to be expected, no difference was noted in any case between the use of sodium and potassium hydroxide, within the limits of experimental accuracy of the titrations. 5-If the weight of sample is so regulated that approximately 15 cc. of alkali solution are required for neutralization, aqueous alkali can be used interchangeably with alcoholic alkali, with no appreciable difference in results within the limits of experimental accuracy.
Vol. 14, No. 1
&In the case of a material with a very high acid number (above loo), such as a fatty acid, there is evidence of some hydrolysis when aqueous alkali is used with alcohol-benzene as a solvent, and alcoholic alkali should be used for titration. TABLE11-ACID VALUESOF MIXTURESOR OIL AND FATTYACID 7 Value-----Value Found in Alcohol-Found in Alcohol Benzene 2' with Aqueous with Alcoholic with Aqueous with Alcoholic KOH NaOH KOH NaOH KOH NaOH KOH NaOH TUNG-OILMIXTURES .1 15.33 14.40 14.37 14.72 14.20 15.22 15.33 15.38 15.41
g -zg
i2
2 3 4
29.25 28.3 59.1 58.8 99.3 99.2
28.3 58.5 98.9
28.7 55.9 99.0
28.6 58.3 98.7
29.3 59.2 99.3
29.1 59.2 98.7
29.4 59.3 99.4
29.3 59.2 99.2
LINSEED-OIL MIXTURES
1 2 3 4
10.61 24.22 53.2 100.4
10.45 23.76 52.86 100.2
10.41 24.01 52.88 99.6
10.55 10.42 10.54 10.52 10.51 10.60 24.10 23.85 24.13 24.25 24.32 24.20 52.97 52.85 53.15 53.13 53.05 53.18 99.9 100.0 100.6 100.2 100.6 100.5
1 2 3 4
11.29 11.07 25.4 25.07 50.7 50.4 101.5 101.7
11.05 24.79 50.5 101.4
1 2 3 4
15.93 29.7 60.7 102.8
14.81 15.33 15.53 15.75 15.87 15.75 15.98 28.33 28.25 28.75 29.32 29.13. 29.25 29.50 59.8 59.7 60.3 60.4 60.3 60.4 60.6 102.2 102.0 103.0 101.8 102.2 102.8 103.2
COTTONSEED-OIL MIXTURES
15.36 28.42 60.2 102.0
11.25 11.22 11.39 11.33 11.65 35.00 25.03 25.40 25.32 25.21 50.4 50.6 50.6 50.6 50.8 100.9 101.6 100.7 101.3 .100.6
11.34 25.26 50.8 101.4
TUNGOIL-ROSIN MIXTURES
Vapor Pressure Determinations on Naphthalene, Anthracene, Phenanthrene, and Anthraquinone between Their Melting and Boiling Points'#z By 0. A. Nelson and C. E. Senseman COLORINVESTIGATION LABORATORY, BUREAUOF CHEMISTRY, WASHINGTON, D. C.
A search of the literature on vapor pressures reveals the fact that very few determinations have been made on most of the solid hydrocarbons between the temperatures of their melting and boiling points, or above. In view of this fact and also in response to the increased demand for more reliable physical constants, arising from recent researches into different types of reactions both in the liquid and vapor phase, the problem of determining the vapor pressures of some of the more common compounds was undertaken. I n this paper the method employed will be discussed, and some of the results obtained in naphthalene, anthracene, phenanthrene, and anthraquinone will be. tabulated. I n subsequent publications the results on other compounds, or mixtures of compounds, which are now under investigation will be given. Up to the present time vapor pressure determinations of compounds of the type in which we are interested seem to have been limited to comparatively low temperatures. Ramsey and Young3 determined the vapor pressures of ~ of a camphor between 0" and 180" C.; V a n ~ t o n e ,that mixture of camphor and borneol between 78" and 185" C., while Allen6 worked with naphthalene between 0" and 130" C. Perman and Davis6 determined the vapor pressure of naphthalene, and of mixtures of naphthalene and p-naphthol at 70" C., and Barker' determined the pressures of naphthalene at 20", 30", and 40' C. From the vapor pressure curves obtained by Stelzner,8 it appears that this investigator determined the vapor pressure of naphthalene between 75" and 170"and extrapolated the curve to 218" (b. p.) while in 1 Presented before the Division of Dye Chemistry at the 6lst Meeting of the American Chemical Society, Rochester, N. Y.,April 26 to 29, 1921. 2 Published as Contribution No. 53 from the Color Investigation Laboratory, Bureau of Chemistry, Washington, D. C . 8 Phil. Trans., 1884, I, 34. 4 J . Chem. Soc., 97 (1910),429. 6 Ibid., 77 (1900), 412. a Ibid., 91 (1907), 1114. 7 Z . physik. Chen., 71 (1910),235.
*
Dissertation, Erlanger, 1901, "Uber den Dampfdruck fester K6rper" (original article not available).
the case of anthracene observations were made for every 10" between 160' and 260" C., and on anthraquinone between 224" and 320". It appears, therefore, that in no case did the temperatures of the experiments even approximate the boiling point of the compounds or mixtures under investigation.
METHODSOF MAKINGVAPORPRESSURE DETERMINATIONS The static method of vapor pressure measurement and the dynamic, or air current method, have been used with different modifications so long and with so much success as t o become almost standard. Other methods have been proposed, such as the optical method devised by C. and M. Cuthbert~on,~ based on the assumption that the refractivity of a vapor was proportional to the vapor pressure; or the hygrometric method devised by Forbes.lo The dynamic method is most suitable for low pressures and low temperature work, and has been used with varying degrees of success by Regnault,l' Idnbarger,12 Perrnan,ls Derby, Daniels and Gutsche,l* and others. The method consists essentially in passing a known volume of air o r indifferent gas over the substance whose vapor pressure is to be determined, and by determining the amount of substance carried over, the vapor pressure is readily calculated from Dalton's law of partial pressures. The air drawn through the apparatus must necessarily be saturated with the vapors, and herein lies one of the chief difficulties. The temperature of the saturator must be kept very constant for considerable periods in cases where the substance under investigation has a low vapor pressure, and this alone is not easy to accomplish especially if the required temperature is comparatively high. Even if constant vapor baths are used, a change of 5 or 10 mm. in the atmospheric pressure Proc. Roy. SOC.London, A , 85 (1911), 305. Chem. News, 106 (1912), 88. 11 Ann. chim. fihys., [3]15 (1845),129. 12 J . Am. Chem. SOC.,17 (1895), 615. 18 Pmc. Roy. Sac. London, 78 (1903),72. 14 J . Am. Chem. Soc., 86 (1914), 793. 9
10
THE JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
-Jan., 1922
i s sufficient to cause an appreciable change in the boiling point of the liquid, and hence in the temperature of the vapor baths. The old static method offers some advantage over the dynamic, but is by no means without objectionable features. Here again the question of maintaining at a constant temperature a long mercury-filled tube (750 mm. or more) presents itself, and also that of expelling the last traces of air or other impurities that may be dissolved in the mercury or absorbed on the inner surface of the glass tubing. For a more detailed and critical discussion of the merits and demerits of the dynamic and static methods of vapor pressure determination, the reader is referred to the work of Smith and Menzies.15 The other methods mentioned above, as well as the dew-point and tensimetric methods, have rather limited applicability and need not be discussed in this connection.
APPARATUS The apparatus used throughout this work was a submergedbulblet, vapor pressure apparatus, as developed by Smith and Menzies. This method seemed to offer a number of advantages not found in any of the others: the temperature could easily be controlled and the pressure could be read off directly on the manometer, thus eliminating errors due to temperature variations, insufficient stirring of the thermostat, or in condensing or absorbing and analyzing vapors, as in the air current methods. The method is also comparatively rapid, since a series of determinations may be completed in one day. The apparatus is shown diagrammatically in Fig. 1. Instead of using an open-end pressure gage, a manometer a trifle over 1 meter in length was made from Pyrex glass tubing of 8 mm. inside diameter. The mercury used in the manometer was carefully purified by shaking with nitric acid and further by distilling three times under vacuum. Before the manometer tube was sealed off, it was very thoroughly cleaned with hot chromic acid cleaning solution, rinsed with distilled water, and dried by heating while a current of dry air was drawing through. After being f l e d with the mercury the manometer was carefully boiled out in order to expel all foreign materials which might be dissolved in the mercury or absorbed on the inner surface of the glass. The boiling out process lasted over 2 hrs., under pressure of approximately 3 mm. Not the slightest indication of air bubbles could be detected anywhere along the tube. The difference in levels of the mercury in the manometer arms was measured by means of a meter stick graduated in millimeters. The accuracy of the calibrations was checked against a standard steel tape, and found to differ by about 0 . 5 mm. in 1000. The temperature of the manometer was observed and the readings were corrected accordingly, taking the value of the cubical coefficient of expansion of mercury given in the Smithsonian tables (0.0001818). The manometer readings were made with the naked eye and were correct to 0.2 mm. The apparatus, not including the heating device and thermostat, was fastened to a board 24in. X 13 in. and consisted essentially of three parts: manometer, A; glass connections all in one piece, and isoteniscope, H. The bottle, G, was evacuated to about 2 mm. before each run was made and was used for lowering the pressure in the system by opening stopcock E. A pressure bottle (not shown) was used for raising the pressure in the apparatus by opening the 3-way Cock, D, which was also connected with the atmosphere. I n cases of pressures below atmospheric the pressure bottle was not used, but D was turned so a~ to admit air directly from the atmosphere. A small hand pump was used
*
16
J . Am. Chem. Soc.. 82 (1910). 32.
59
to produce the necessary pressure in the bottle or in the apparatus.
J
FXQ.1
The isoteniscope, or rather “dynamic isoteniscope,”’6 was made of heavy Pyrex glass and was about 45 cm. in length. The bulb containing the confining liquid1’ was 50 mm. long and 30 mm. in diameter. The side bulb containing the substance was also made of Pyrex glass, but with much thinner walls, and had a diameter of about 20 mm. This part of the apparatus could readily be detached from the rest by removing clamp I which held it in position; and since it was connected to the main part of the apparatus by a piece of rubber tubing it could easily be removed for refilling. All rubber connections were short and held a high vacuum for considerable periods. To test the different connections, as well as the stopcocks, the apparatus was evacuated to about 2 or 3 mm. and left until the following day, when an increase to only about 10 mm. was observed. The thermostat and method for observation of equal pressure in the side bulb containing the substance under investigation and the manometer are shown in Fig. 2. A beaker of one and one-third liters capacity was used to hold the liquid bath (glycerol for naphthalene and the eutectic mixture of sodium and potassium nitrates for the higher boiling compounds) and was heated by means of an electric heater. This heater was made by winding No. 22 asbestoscovered nichrome wire on a glass beaker with a diameter a trifle larger than the one to be used throughout the observations. This wire was covered with a layer of alundum cement and dried in an electric oven. When perfectly dry it was placed in a cubical wooden box 9.5 in. on a side and insulated with packed asbestos shreds. With this amount Smith and Menzies, LOG.cit., 1448. I n each determination the material constituting the confining liquid was the same as that the vapor pressure of which was being measured. 18
17
,
T H E JOURNAL OF INDUXTRIAL AND ENGINEERTNG CHEMISTRY
60
of insulation it became an easy matter to maintain constant temperature of the liquid bath long enough to bring the pres-
FIG. HEATER B-PYREX BEAKER( 1 , 3 I,.)
2 D-ISOTENISCOPE E-SAMPLEBULB
C-STIRRER
F-CONFINING-LIQUID
A-ELECTRIC
BULB
I-INSULATION: ASBESTOSSHREDS
sures to equilibrium. By means of a 2-way switch, connections were made with both 110- and 220-volt circuits, the latter being used to boost the temperature to save time. I n order t o enable the worker to observe when the levels of the liquid in the tube leading from the side bulb of the isoteniscope and that of the confining liquid were the same, two holes about 1 in. in diameter were made, directly opposite, through the sides of the electric heater and the surrounding insulation. By adjusting the position of the isoteniscope in such a way that the bulb containing the confining liquid was directly in line with these holes, and hy placing an electric light a t the opening of one of them, observations could very easily be made through the other. The bath liquid was kept in violent motion by a stirrer revolving at high speed. TEMPERATURE MEASUREMENT It is well known that for temperatures between 250" and 350" or 375' ordinary mercury thermometers cannot be relied upon. From calibrations made by the Bureau of Standards one often observes a correction of from & l oto 1 2 ' over a range of 50" C. Such errors are not often of much consequence in ordinary work, but in work similar to this an error of 0.1" C., near the boiling point of naphthalene, for example, would produce an error of 1.7 mm. in the vapor pressure. Smith and Menzies used a platinum resistance thermometer, and were able to observe temperature variations of from 0.1 to 0.01' C. Inasmuch as such an instrument was not available for the present investigation, a multiple junction copper-constantan thermoelement was made, and the temperature calculated from the e. m. f. developed.
Vol. 14, No. 1
From the work of Adams of the Geophysical Laboratory's this method of temperature measurement is shown to be perhaps the most reliable, as well as the most accurate, so far developed. Adams observed that with a single copperconstantan couple a temperature variation of approximately 0.02" C. would cause a change of 1 microvolt in the e. m. f. produced, or with a sensitive potentiometer R temperature change of 0.01' could readily be observed. Not having available a galvanometer sensitive enough to register such minute changes in e. m. f., instead of using a single couple, the writers employed a multiple element, consisting of five couples connected in series. The e. m. f. with such an arrangement, using 0' for the cold junction temperature, varied from 0 microvolts at 0" to about 94,000 microvolts at about 380", or a change in e. m. f. of nearly 250 microvolts for a change of temperature of 1" C. The constant boiling liquids used in calibrating the thermoelement were water for 100" C., naphthalene for 217.95", and benzophenone for 305.9". Corrections in the boiling points of these compounds were made for changes in atmospheric pressures. To make certain that our calibrations were correct, the results obtained in our laboratory at the temperature of the boiling points of water and naphthalene were checked against observations made on our thermocouple at the Geophysical Laboratory, under the supervision of Mr. Adams. PURIFICATION OF MATERIALS The naphthalene was obtained pure from the stock rooms and showed a boiling point of 217.95" at 760 mm. The anthracene was obtained from the commercial product (about 85 per cent) by repeated sublimations and two crystallizations from solvent naphtha, two from benzene, and one from 95 per cent alcohol. The carbazol was removed by fusing with sodium hydroxide and potassium hydroxide before the first sublimation. The final product showed a beautiful purplish fluorescence and had the same melting point as the Kahlbaum product used in one of the runs. Phenanthrene mas purified in the same way as the anthracene, and had a melting point of 100" C. The anthraquinone was crystallized twice from benzene and dried for 5 hrs. at 120' C. before using. TABLE I-NAPHTHALENE Vapor Pressure Temperature Mm. c. 181.20 11.9 185.34 15.5 188.30 18.5 196.96 22.9 198.53 28.7 200.50 35.9 205.78 38.3 206.00 58.7 212.17 71.2 213.30 103.5 217.34 165.1 217, 8 l 187.1 221.4.3 260.8 290.0 LOC.cit., 412.
Temperature
c.
87.47 95.001 100.00 104.39 109.65 114.70 117.15 128.06 133.72 144.45 15s. 95 163.13 175.10 178.44 1 Allen,
Vapor Pressure Mm. 310.6 347.6 376.5 464.1 482.1 505.7 576.2 5x1 . 9 667.8 682.7 755.8 759.2 825.2
TABLB IT-ANTHRACENE Temperature
c.
18
Vapor Pressure Mm. 52.7 52.7 60.2 62.1 69.6 86.5 113.4 129.5 135.5 142.5 169.3 175.0 203.2 198.2 247.7 279.0 303.0
Temperature
c.
297.38 298.22 304.35 310.31 318.20 321.29 325.47 329.47 335.52 337.14 337.70 340.58 341.57 341.70 342.05 343.25
Am. Inst. Mining Met. Eng., Bulletin 163 (1919)
Vapor Pressure Mm. 317.7 319.1 363,9 415.6 488.1
+e.p
0na.o
612.2 674.4 692.7 697.6 738.9 766.4 757.3 761.2 778.2
Jan., 1922
T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY TABLE 111-PHENANTHRENE
Temperature
c.
232.34 233.54 246.59 249.14 264.73 269.89 281.33 262.73 294.57 295.37 299.88
Vapor Pressure Mm. 62.2 65.4 94.5 101.5 151.4 172.4 226.1 234.1 307.4 311.4 340.2
Temperature e
c.
300.91 309.44 308.64 312.62 319.27 321.24 332.11 333 IO8 339.91 340.41 340.59
Vapor Pressure Mm. 350.9 420.3 4414.8 446.0 510.7 531.5 654.4 664.6 754.3 762.3 764.2
Temperature 0
c.
Temperature O
c.
Temperature
c.
FIG.3
Temperature
c.
285.56 286.71 292.74 295.30 302.80 306.74 311.43 315.38 319.83 321.70 325.01 329.22 330.96 334.34 335.35 339.80 344.30
TABLE IV- .AN'THRAQUINONE Vapor Pressure Tempzrature Mm. C. 346.11 104.0 108.0 349.03 122.2 351.14 133.5 357.00 156.0 361.18 172.6 362.82 189.8 364.54 209.5 367.33 230.6 370.66 241.5 373.71 377.53 259.4 378.71 282.7 379.73 296.4 381.21 317.5 382.14 323.4 352.6 383.18 368.0
Vapor Pressure Mm. 402.0 426.0 446.2 500.0 546.6 562.3 579.2 615.8 656.0 665.4 733.1 746.4 759.0 779,4 791.6 604.7
RESULTS OBTAIXED The results obtained in the vapor pressure determination on naphthalene, anthracene, phenanthrene, and anthraquinone are given in Tables I, 11, 111,and IV, respectively. Fig. 3 shows the vapor pressure curves of these compounds using the above values. The above observations were plotted on 80 em. x 100 em. coordinate paper, and the pressures for intervals of 5' were read from these curves. These Observations are tabulated in Tables V to VIII, inclusive, and are intended to show the mean values of all our observations on the compounds worked on thus far. It should be pointed out that since it is hardly possible to read a manometer closer than to within 10.1 or 0.2 mm. without the aid of a cathetometer or a vernier arrangement, the per cent error is necessarily much greater where the, pressures are low; while a t higher pressures the large variation due to small changes in temperatures makes observations difficult at these points. It was, however, much easier to obtain good checks at the higher pressures than at the lower, for, as pointed out in the first part of this paper, the temperature was controlled without much difficulty. As may be seen from the above tables and curves, the boiling points of these compounds are as follows: Kaphthalene 217.95' (taken from literature and used in calibrating thermocouple), anthracene 342 O, phenanthrene 340.2O, and anthraquinone 379.8'. The results obtained on phenan-
Temperature O
c.
TABLE V-NAPHTEIALENE Vapor Pressure Temperature Mm. c. 9.9 155 12.0 160 14.9 165 18.5 170 23.0 175 180 26.5 35.0 165 42.7 190 51.8 195 62.4 2n0 74.6 205 88.7 210 104.8 215 123.3 218 220 TABLE VI-ANTHRACENE Vapor Pressure Temperature Mm. c. 42.6 290 49.5 295 57.3 300 66.1 305 76.0 310 67.1 315 99.6 320 113.5 325 129.1 330 146.5 335 165.6 340 187.3 342 211.0 345 237.2 TABLE VII-PHENANTHRENE Vapor Pressure Temperature Mm. c. 58.3 290 68.1 295 79.0 300 91.1 305 104.4 , 310 119.2 315 135.5 320 163.7 325 173.6 330 195.7 335 220.0 340 246.7
61 Vapor Pressure Mm.
Vapor Pressure Mm. 265.9 297.5
Vapor Pressure Mm.
TABLE VIII-ANTHRAQUINONE Vapor Pressure Vapor Pressure Temperature Mm. Mm. c. 354.5 103.0 340 392.9 116.2 345 435.5 131.3 350 461.9 147.8 355 531.7 166..0 360 585 4 166.0 366 643.4 207.9 370 703.0 232.0 375 760 258.5 379.6 763.4 287.5 380 319.4
threne and anthraquinone agree very well with those given in the literature, namely, 340' and 380" C., respectively. For the boiling point of anthracene the literature gives 350' and 351' C.19 but in no case was this temperature reached before the pressure reached points much above 760 mm. Further t o verify the observations on anthracene at this temperature, the writers made three sets of duplicate determinations on three different samples of anthracene: two, on a sample prepared by Dr. K. P. Monroe, formerly of the Bureau of Chemistry, two, on the product purified from commercial anthracene as outlined above, and two, from a sample of Kahlbaum's. A large number of observations were made on each of these samples at about the boiling point, with an agreement well within the limits of experimental error.zO Boiling point determinations were also made according t o the method described by Mulliken, using an Anschute thermometer, with results that again agreed with those given above, as obtained by vapor pressure determinations. 19 Landolt-Bbrnstein, "Physikalisch-chemische Tabellen;" Mulliken, "Identification of Pure Organic Compounds." 20 The experimental error referred t o here is the error introduced in reading the manometer, as pointed out above, and a slight error due to inability t o observe variations in e. m. f . to less than 2 microvolts corresponding to approximately 0.008° C. It should be noted, however, that the change in pressure corresponding to a change of O.O0So C. in the temperaturq a t about the boiling point of anthracene is of the order of 0.10 mm. so the error in temperature reading becomes negligible.
T H E JOURNAL OF IhTDL'XTRIAL AND ENGINEERING CHEMISTRY
62
SUMMARY A brief resum6 of previous vapor pressure determinations has been made. A detailed description has been given of the method employed in obtaining vapor pressure values for naphthalene, anthracene, phenanthrene, and anthraquinone, and tables
Vol. 14, No. 1
and curves of observed vapor pressures of these compounds have been recorded. Boiling point determinations have been made on anthracene, phenanthrene, and anthraquinone with the following results: Anthracene, 342" C.; phenanthrene, 340.2" C.; anthraquinone, 379.8" C.
Experiments with Heat Interchangers' By F. Russell Bichowsky DEPARTMENT OF CHEMISTRY, UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA
In liquid air machines and other refrigerators which depend on the Joule-Thomson effect for cooling, the efficiency depends, for a given intake pressure, temperature, and rate of flow of the gas, on the character of the heat insulation, and especially on the efficiency of the heat interchange between the comparatively hot incoming and comparatively cold outgoing gas. In a perfect heat interchanger, the gas entering the interchan'ger and the gas leaving the interchanger will have the same temperature. Assuming the intake temperature of the gas (in this case 02) to be 2138" A,, and the intake pressure to be 200 atm., and assuming perfect heat interchange and perfect heat insulation, and taking for the value of the Joule-Thomson effect under these conditions -50°, for the molal heat capacity of the gas a t 1 atm. G.7, and for the heat of vaporization per mole 1800 cal., it ran be shown that 11 per cent of the gas will be liquefieda2 If the outgoing ga8 leaves the interchanger a t temperatures less than that of the incoming gas, a similar calculation will show that the yield of liquid 0 2 (and the same values hold approximately for liquid air and liquid Nz) will be decreased 20 per cent for each 10" difference of temperature between outgoing and incoming gas. Ordinarily, even for the comparatively poorly insulated, small-size liquefiers found in many laboratories, the loss of efficiency due to poor thermal insulation is small, compared with that due to poor interchange. The heat interchanger commonly used on liquid air machines consists of a coil of one or more copper tubes either wound one tube inside the other, as in the original Linde design, or, as is more common in laboratory interchangers, of the Hampton type, in the form of flat coils, the firzt coil being mound from the center out and the next from the outside in, either one tube being used or several tubes wound in parallel. In the Linde design the compressed gas, after expansion a t the lower end of the coil, passes back the entire length of the coil through the annular space between the inncr and outer tubes. I n the Hampton type, the gas, after expansion, passes back over the tightly wound coil through the interstices between layers left during winding. Oneeighth inch 0. d. drawn soft copper tubing is about as small as is practical to use, and one-fourth inch 0. d. copper tubing is a convenient size. To study the efficiency of heat interchange in such small tubes between the walls and the rapidly moving high pressure gm, the apparatus shown in Fig. 1 was constructed. The wire AC was of tested No. 40 constantan which was carefully stretched so as to be exactly central in the tube. The small leads were No. 40 copper, the whole forming a differentid thermoelement giving the difference of temperature of the gas between A, B, and C. The initial temperature was given by a thermoelement not shown. The mean inside diameter of the tube was 0.124 in. (0.315 cm.), the outside 0.251 in. (0.638 1 Received
March 7, 1921. is based on the equation 0 8 (g. 298-50' A,) =zOa(l, 90' A.) (1-x)Oz (9. 298" A.); 4H-0. Here z is per cent of gas liquefied and H is heat content. Details will be given by Lewis and Randall, "Treatise on Thermodynamics."
+
* This
cm.). The length between junctions A-B and B-C was 1.0 ft. (30.5 cm.). Table I gives typical results of many tests. I n this table, temperatures are given in degrees Centigrade absolute, pressures in atmospheres, rate of flow in cu. m. per min. free gas. The figures in parenthesis in Columns 4 and 7 are corresponding values in cu. ft. per min. and O F. per ft. per deg. TABLEI Intake Temp. TEmp. of Bath Pressure Rate of Flow A. OA. Atm. Cu.M./Min.
290 240 290 240 290 290 240 290
90 90 240 90 240 90 90 240
200 200 200 100 100 200 200 200
0.93(33) 0.93(33) 0.93(33) 0 93(33 0:93 331 0.47{16.5) 0.47(16.5) 0.47(16.5)
Tem A-C?
33 25 8 24 8 68
42 15
Diff Temp Modulus A-E Deg.jM.lDeg.
17
0r26 (0.085)
11 4
12
4 35 20 8
0 42 0 13) 0 : 5210: 16)
The first six columns are self-explanatory; the last column gives the temperature modulus, i. e., the fall of temperature per nieter of tube per Centigrade degree difference of temperature between the temperature of the bath and the temperature of the incoming gas, found by dividing the values in Column G by the temperature head, i. e., by the temperature of the bath minus the intake temperature. These results, which are only approximate, show that the temperature drop per meter of tube is independent of the pressure, inversely proportional to the rate of flow, and proportional to the temperature head from bath to incoming gas. Knowing the modulus as defined above for a given sized tubing and given rate of flow, it is possible to calculate the length of that tubing which will be necessary to construct an ideal interchanger of given thermal efficiency. =temperature of incoming gas =temperature of gas just before expansion = tempeEature after expansion (for liquid air machines this will be T8 temperature of liquid air) T4 =temperature of gas leaving exchanger Cgi =molal heat caparity of incorning gas, under pressure Pi at any point along interchanger c g 0 =molal heat capacity of outgoing gas, under pressure Po at same point along interchanger ti and to = temperatures of incoming and outgoing gas at same point Mi =mass of gas, in moles, entering interchanger in any interval of time Mo =mass of gas leaving interchanger in same interval Then for a liquid air machine Mi-Mo = A , the mass of air liquefied in that @interval;or, choosing the interval so that Mi = 1, and assuming that the liquefier has been running long enough so that conditions do not change with the time, I - M o equals the efficiency of the liquid air machine. Now Cgi and Coo will in general be functions of the temperature, i. e., cgi = fgi (T) and Cg, fg, (T). The function will depend on kind of gas and pressure. This may be determined by experiment. Let 1 be the length of the interchanger, and let p be the temperature modulus as defined above, i. e., the drop of temperature per unit length per degree temperature head. Now the heat transferred from the incoming to outgoing gas for any small segment of the interchanger is Let Ti
Tz
-
(ti
-10)Pdl
where dl is length of segment. This equals MCPo dt and 4- CPi dt, where d t is change of temperature of the gas in length dl. Integrating gives:
