1038
HERRICK L. JOHNSTON .4ND KENNETH E. MCCLOSKEP
VISCOSITIES OF SEVERAL COMMON GASES BEl'WEEK AND ROOM TEMPERATURE
WOK.
HERRICK L. JOHNSTOX AKD KENNETH E. McCLOSKEY Department of Chemistry, The Ohio State University, Columbus, Ohio
Received October 3, 1930
Although considerabl(~work has been done on tlit. viscosities of gases below the ice-point', the data h a w usually been taken a t widely scparated points on the temperature scale and would seem, with a few notable exceptions, to be no11(~too reliable. In connectioh wit,h a program of accurate low-temperature heat-capacity nicasurementx on gases by the velocity of sound method, the authors havc considcrcd it advisable to carry out a series of viscosity mc~asurernentsin the lowtemperature rangc. In addition, it was felt that accurate yiscosity data would furnish a worthwhile contribution to the study of interrelationships among heat capacities, thermal conductivities, data of state, viscosities, and interniolecular forces. This paper deals with a description of the method and apparatus used, together with results obtaiiied on hydrogen, air, oxygen, nitrogen, nit,ric oxide, nitrous oxide, carboil dioxide, and methanc. METHOD AND .\Pl'.\It.\TIJS
h careful consideration of thc problem of measuring gas viscosities over the low-temperature range leads ultimately to the oscillating-disk method of Maxwell (21, 10, 8, 25). The apparatus (figurc 1) was patterned after that of Sutherland and Maass (25), but included certain refinements which it was felt would increase t8hereliability of the results, especially in the measurement &ndcontrol of temperature. Temperat u i ~measuwnent and lemperatirre control Tempyat,ures were determined by means of a copper-constantan thcrmocouple soldered directly to the bottom of the lower fixed disk. This had the advantage of measuring the temperature of thermally conducting metal adjacent to tho portion of gas whose viscosity was determined. Subsequent measurements showed that the temperature of this region differed significantly from that of the bath, owing in part to conduction of heat by the gas which fills the central column of the apparatus. Thc thermocouple employed was one of several standardized in this laboratory against the Berkeley temperature scale (5) through the intermediate standard couple, designated as couple 101, calibrated by Milner and. Greensfelder (17). Our scale is believed accurate to zk about 0.05', which is better than our requirement. The couple was wound loosely around the supporting screws for several turns, to eliminate temperature gradients
VISCOSITIES O F CASES
1039
near the junction, and was taken out of the apparatus through a de Khotinsky seal a t the top of the side tube F. A large Dewar flask contained the bath for regulating the temperature of the gas. An air-driven stirrer, supported independently of the mount that held the apparatus, was run slowly enough to prevent noticeable vibrations
FIG.1. Apparatus
Liquid oxygen was used for the bath at 90°K. At 118°K. a freezing mixture of dichlorodifluoromethane was maintained by inserting into the bath a copper flask rontaining liquid air to a suitable level. Between 130' and 150°K. a thin-nerked copper Dewar flask was used with a bath of dichlorodifluoromethane. Regulation of the liquid air level in the Dewar flask and of the hydrogen pressure between its walls proved a sufficient means t o offset heat leak into the bath or to reduce the warming rate to a few tenths of a degree per hour. Above 150°K. the bath was thermos t a t t d with the iise of accessory apparatus patterned after the precision
1@ko
HERRICK L. JOHNSTON AND KENNETH E. MCCLOSICEY
cryostat of Scott and Brickwedde (24). Thermostatting was usually better than f 0.05'. Dichlorodifluoromethane was employed aa bath liquid to a temperature of 170'. Above this temperature a bath with the following composition was used: 19.4 per cent chloroform, 44.7 per cent ethyl bromide, 22.5 per cent trichloroethylene, and 13.9 per cent s-dichloroethylene. For all runs two temperatures were read and recorded, both before and after the viscosity measurements: namely, that of the silver disk by means of the standard couple previously referred to, and that of the bath by means of a second copper-constantan couple submerged in the liquid. The two readings were usually not identical. In thermostatted runs the temperature of the disks usually exceeded that of the bath by a few hundredths of a degree owing, presumably, to heat conduction by the gas in the vertical column of the apparatus. In some trial runs in which the bath was permitted to warm at the rate of 2' or 3" an hour the conditions were reversed, the silver disks lagging behind approximately 1'. Rapid heating of the bath (1' per minute) produced temperature differences of 6' to 7' between the bath and the disks. These results indicate the necessity of measuring temperatures directly at the disks, in reporting viscosities. Other variations f r o m the design employed by Sutherlund and Maass ( a ) I n order to maintain constant spacing between the oscillating disk and the fixed disks, in spite of temperature changes in the lower part of the apparatus, the section of brass rod below the ivory segment was made the same length as the three long screws which support the fixed disks. The desirability of maintaining constant,spacings is shown by an equation given by Keesom and van Itterbeek (15)
C =
W'
(di
+ dl)/4Ididn b
(1)
in which C is the apparatus constant (cf. equation 2), r the radius of the oscillating disk, dl and dz the distances which separate the oscillating disk and the upper and lower fixed disks, respectively, and I the moment of inertia of the oscillating system. ( b ).Spiral springs of brass slip over the loiig brass supporting screws and bear against special washers placed just under the glass risers. These prevent permanent displacement of the fixed-disk assembly as the result of successive contractions and elongations of the supporting screws consequent on temperature changes in the bath. (c) The hook and grooved eyelet, placed by Sutherland and Maass a t the upper end of the suspension wire, were placed by us at the bottom, where they could be reached through the open window with a curved pair of tweezers. The window was cemented in place with a non-volatile
1041 * cement, which could be easily softened with a flame. This variation in design was a considerable advantage for purposes of assembling or repairing the apparatus, since the whole suspension could be changed without removing the apparatus from its supports or necessitating adjustments below the window. (d) Amplitudes of successive oscillations were observed by means of a telescope with cross hair, with the aid of an illuminated scale. The scale was set a t approximately 10 feet from the apparatus, to obtain high sensitivity. To prevent any distortion of the mirror which might result if it were cemented directly to the brass rod, it was tied firmly with silk thread to a thin piece of cork which, in turn, was cemented to the rod by means of shellac. A small galvanometer mirror, which was ground to dimensions of about 2 mm. by 3 mm., was employed. The apparatus was firmly clamped in a wooden support attached to a 3 ft. by 3 ft. concrete pillar which formed a portion of the foundation of the building. VISCOSITIES O F GASES
PREPARATION .4ND PURIFICATION O F GASES
Hydrogen, investigated largely to test the reliability of the apparatus, was taken from a commercial tank of electrolytic hydrogen and was purified by slow passage through charcoal cooled with liquid air. Preliminary treatment of the charcoal involved evacuation at a dull red heat and subsequent washing with hydrogen at the same temperature. Air, taken from outside the laboratory, was freed from carbon dioxide and water vapor by slow bubbling through concentrated potassium hydroxide solution and concentrated sulfuric acid, followed by passage first over stick potassium hydroxide and then over phosphorus pentoxide. Oxygen was prepared and purified by the method outlined by Giauque and Johnston (7). The electrolytic cell used operated on a current of 5 amperes. Nitrogcn was prepared according to the procedure outlined by Giauque and Clayton (6). Nitric oxide was prepared by the method of Johnston and Giauque (13), using the preparation and purification system set up by Johnston and Weimer (14). Nitrous oxide was prepared by the procedure folloffed by Johnston and M’eimer (14). Carbon dioxide was prepared by the modificatioii of the method of Maass and Cooper (19) and by the modification of the method of hleyers and Van Dusen (22) employed by Long (18). Methane was prepared by the Grignard reaction, special precautions being taken to free the gas from ether vapor. The methane was fractionated several times in a closed glass system, the end fractiow being
1042
HERRICK L. JOHNSTON AND KENNETH E. MCCLOSKEY
discarded each time. This is essentially the procedure set forth by Duncan and Howe (3). CALIBRATION
Maxwell (21) derived the following fundamental equation for the oscillating-disk viscosity apparatus: 'I = (X - z)/Ct (2) where 7 = viscosity, X = logarithmic decrement, z = wire constant, t = period, in seconds, of one oscillation, and C = the apparatus constant. We can put for the logarithmic decrement:
where L,, is the full amplitude of thc nth oscillp,ion (corrected for noncurvature of our scale) and n takes on the values 1 , 2 , . . . i. Our custom has been to take series of ten oscillations (i = 5) for gas runs. The five values for X thus obtained in a single series ordinarily agreed to within 0.1 of 1 per cent.
W i r e constant To obtain the wire constant, which is a measure of energy losses in the wire alone, the logarithmic decrement was measured with the apparatus thoroughly evacuated. Preliminary to each determination the apparatus was evacuated to a prmsure of mm. of mercury, or under, for from 12 to 24 hr., with the apparatus a t room temperature. The bulb of the apparatus was immersed in liquid air for the determinations. For determinitions of the wire constant, each run consisted of a series of 60 oscillations (that is, i = 30 (equation 3)). Table 1 indicates the degree of reproducibility obtained in the measurement of wire constants. These refer to measurements made within a single day. Although Sutherland and Maass (25) assumed z to remain constant after several hours annealing at lOO"C., our own preliminary measurements indicated small but significant irregularities that could be accounted for only by variations in z. Further investigations revealed ( 1 ) that z decreases normally with use, owing apparently to work hardening of the wire as the result of twisting, and (2) that z is increased markedly if glass blowing is done on or near the apparatus, even though there be little apparent opportunity for the wire to become heated. These observations are brought out clearly in figure 2, for a wire on which numerous determinations of the constant were made over a period of more than two months. Accordingly it was found necessary to repeat determinations of the wire cocstant a t convenient intervals, and to interpolate to intermediate dates. Table 2 is a record of determinations of the wire constant within the period
TSBLE 1 Determinations of the wire constant for suspension I
I
DATE
t
0.000866 0.000854
August 12, 1937
0.000861
Akverage.., , , . , . . . . . . . , . . . . . . . . . . . . , . . . j
0.000860
i I
I
0.0013
x ChV'rnI
0.0010
p
W'K
&I
cilrm. , w m d l f i i r
0.0007 0
20
40
60
TIME IN DAYS FIG.2 Variations in the mire constant with time and with experimental adjustments
TABLE 2 Deterinanatzons of the wire constant for suspenaaon II
(a) Determinations mior t o readjustment of zero settina September 10, 1937 September 27, 1937
0.000734
0.000676 ~~
~~
(b) Determinations subsequent to readjustment of zero setting I October 1, 1937 0.000747 October 10, 1937 I 0.000663
* There can be no doubt that these systematic variations in z are real and t h a t proper method of interpolation has been pursued in choosing 2's to use with the viscosity data: namely, by using curves rough-drawn to the shape of that in figure 2. However, the entire effect is small. If the evidence of figure 2 and the reproducibility exhibited in successive determinations, as in table 1, were neglected, and the four values of table 2 were averaged as though they represented an experimental spread of error, the viscosity value most affected-that of methane a t 90O-would be changed by only 0.25 of 1 per cent. 1043 R
1044
HERRICK L. JOHNSTON AND KENNETH E. YcCLOSKEY
during which the majority of the viscosity data were collected. Each value is an average of several determinations, as in table 1. The wire (suspension 11) had been previously annealed in situ a t 100°C. a&r the rest point was adjusted and all glass seals completed. During the annealing proceas hydrogen was held in the apparatus to increase heat transfer between the wire and the condenser walls. The wire constant decreased slowly with time. Between September 27th and October 1st the rest point was readjusted, which necessitated opening and resealing the glass tubes C and D (figure 1). The wire was reannealed before the new calibration on October 1st. Apparatus constant The apparatus constant was determined by measurements of logarithmic The viscosity of air decrements in air a t temperatures close to 296.1'K. poises a t 296.1'K. This is the average of was taken aa 7 = 1833.0 X t,he following published results,: 1829.2 X 10-7, Houston (11); 1834.9 TABLE 3 Corrections to the viscosities made necessary by thermal contraction of the metal disks T
__
CORllCFION
'K.
pa cent
300
-0.006 +o. 156 +O .316
200 100
X Kellstrom (16);1834.7 X 10-7,Bond (2);1834.4 x 10-7,MajumBanerjes and Plattanaik (1); 1830.3 dar and Vajifdar (20);1833.3 X X loA7,Rigden (23);1834.1 X 10-7, Fortier (4). This value, which is 0.57 per cent higher than the value of Harrington (9),1822.6 X lo-', which has served as the standard for most of the recent work in the United States and Canada, agrees well with the standard generally accepted in for air at 273.1°K.,corEurope: namely, Vogel's (29)7 = 1724 X for air a t 296.1'K. responding to t) = 1832 X Determinations of the apparatus constant, with air, were repeated at 4- to 5 d a y intervals during the period that active measurements of the several gases were in progress. Measurements on six different days prior to the readjustment of the zero setting averaged C = 5.368with deviations from the mean equal to about 0.1 of 1 per cent. Three determinations subsequent to the readjustment of the zero setting averaged 5.380 with deviations of only 0.05 of 1 per cent from this mean. Within limits of experimental error, the wire constant appeared to be independent of time, but was somewhat affected by the readjustment of the zero. The value
1045
VISCOSITIES OF GASES
5.368 was therefore employed as the apparatus constant for all data taken prior to October 1, 1937 and 5.380for all data taken subsequent to that time. THE DATA
The experimental data are given in tables 4 to 12 and are shown graphically in figure 3. These include a small correction made necessary at TABLE 4 Viscosity of hydrogen T
DATl
___ ___
October 5, 1937
90.28 390.6 391.2 390.6 390.9 117.48 474.2 474.0 474.1 131.63 513.0 513.0 132.69 515.4 515.4 145.30 548.2 549.0 548.6 Q
1 1
200.67 683.1 682.1 682.6
AQ1
_x_107
216.06 717.2 718.2 717.7 231.07 750.7 751.5 751.1
1
11
244.99 780.6 781.7 781.1 259.87 812.4 813.5 813.0 273.23 841.1 842.2 841.7 286.78 869.2 868.5 868.8
169.07 603.9 608.3 606 1 184.01 643.4 639.4 641.4
AVl;n-
q
'K. October 3, 1937
156.94 576.2 575.3 575.7
October 3, 1937
x io7
__
~
'K.
October 2, 1937
I
1
October 1, 1937
299.95 895.6 895.6
Ortober 3, 1937
300.05 896.7 895.3 896.0
~
temperatures other than 296°K. by virtue of thermal changes in the dimensions of the oscillating-disk assembly. The need for this is made' apparent from equation 1, which shows that the apparatus constant will vary directly with r 4 / I and inversely with d1d2/(d, d2). Neglecting the slight difference in the thermal expansion coefficients of brass and of silver &) and the contributions from both brass and silver to the dld2/(d1 portion of the correction, the net effect is that C varies directly with the first power of the linear expansion of silver. Taking the average coefficient
+
+
1046
HERRICK L. JOHNSTON AND KENNETH E. MCCLOSKEY
for silver to be 16.1 X (12) over the temperature interval 90" to 300"K., the magnitudes of the corrections to viscosity are indicated in tablc 3. Wire constants were interpolated to the dates a t which rims were made, in the manner previously indicated. Pressures during the ruiis varied from 500 nim. a t 90°K. to 760 Inm. a t 300°K., except as noted in table 11. An unrecorded run with methane
__
~
T
DATE ~
~
AVERAGE
,x
,xi07
___
107
October 10, 1937
T
DATE
I
I
~
I October 11, 1937
AYEBAGE 'I 107
x 10'
x
'IC.
215.2
1424.4 1423.5 1420.9 1422,9
230.5
1503.7 1502.7 1503.2
245.6
1584.4 1584.6 1584.5
260.3
1655.4 1665.9 1662.0 1661.1
146.19 1011.4 1010.3 1010.9, October 12, l%?
273.2
160.89 1110.2 1099.4 1113.0 1107.5
1725.9 1724.0 1722.8 1724.2
284.6
1776.6 1778.4 1777.5
645.5
0 . 2 8 646.1 645.6
645.9
September 16, 1937 118.40 835.7 834.4
835.0
132.78 928.7 929.8
i j Octohcr 11, 1937
929.3/
I
October 11, 1937
7
~
~
'K.
September 11, 1937 90.22 645.4 644.3 646.7
~- ~-
1
I
183.27 1235.3 I 1 1244.1 1239.9 i 1235.2 12.78.6 1
300.1 1851.3 1851.0 1854.0 1849.2 1851.4
I
201.59 1346.0 1347.8 1343.9 1345.9 1 ~
I
-____
_
_
_
_____ ~
at 90°K. (suspension 1) and a pressure of 78 mm. likew sensible dependence on the pressure. Sutherland and Maass (25) and van Itterbeek (27) have found viscosities to be independent of pressure over much wider limits. Measurements on carbon dioxide were taken with suspension I. At thc time of these measurements variations of the wire constant with time
1047
VIBCOBITIEB OF GASEB
were unsuspected. However, several runs on air ivere taken just prior t o the runs with carbon dioxide and several rwis with methane were made just aftrr the carbon dioxide runs. Comparison with the later data obtained on air and on methane, with ,suspension 11, permitted evaluation of the wire constant values in the earlier rum and, by interpolation, thc value of the wire constant during the carbon dioxide runs. The results obtained were consistent with the direct measurements recorded in tahle 1
-
T
DATE
_____
.
_ - ___
Viscosity of oxygen
_
1x10’
---_
‘K.
September 13,1937
90.28 692.7 692.7
_ AVER-
_
AQE
~
_
_
_
DATE
n x 10’ ~
T
__
qX10’
AYEPAGE
7
~
x 10’
__
‘K. September 14, 193: 215.17 1573.9 692.7 1573.5 1573.7
September 15, 1937 118.81 908.3 909.6 907.8
908.6
131.29 998.0 1000.5
399.4
September 15, 1937 144.94 1099.9 1098.3 September 16, 1937 1097.7 1098.6
273.16 1916.5 1918.9 1919.6 1918.4
September 13: 1937 158.46 1185.6 1184.3 1185.0
September 14, 1937 172.56 1286.4 1 2 0 . 1 1288.2
Septcmhcr 12, 193i 184.61 1373.2 1374.9 1374.0
Septemher 14, 193i 201.49 1483.4 1483.5 1483.5
and the character of variations with time and treatment revealed in figure 2. An apparatus constant was determined at the time of the carbon dioxide runs through. calibration with air at 296°K. On account of this indirect manner of evaluating the wire constant for the carbon dioxide runs, the data are slightly less accurate than were obtained with the other gases. However, the added uncertainty from this source of error should not exceed 0.1 of 1 per cent.
1048
HERRICE L. JOHNSTON AND KENNETH E. JICCLOSKEY
Table 13 gives smoothed values of the riscosities read at 10" intervals from large-scale graphs. ACCURACY O F RESULTS
The average deviation of two hundred and fifty-seven experimental points from the smooth curves of figure 3 is & 0.13 per cent. The precision is somewhat less at low than a t high temperatures. One hundred and three TABLE 7 Viscosity of nitrogen DATE
T __ OK.
AVER-
1x107 ~
AQE
'
DATE
x 107 -_.______ 'IC.
September 18,19:
90.17 631.9 September 19,193 215.75 1381.0 630.9 1380.6 1380.8 631.5 631.4 229.88 1451.9 September 17, 191 118.26 817.5 1455.0 1453.5 815.4 816.4 245.19 1532.1 130.82 890.8 1530.6 1531.3 894.0 892.4 260.13 1603.4 140.98 954.1 1602.5 1603.0 955.6 954.7 273.21 1664.6 155.56 1039.7 1664.2 1046.0 1666.3 1665.0 1039.9 1041.8 September 20,193 285.08 1718.3 169.4 1121.7 1720.6 1719.5 1120.2 1124.7 1122.5 300.05 1785.1 1783.8 1785.8 1784.9 September 19,193. 184.721209.1 1210.9 1210.0 September 18,193 300.07 1788.4 200.16 1295.2 1785.5 1787.0 1301.2 1298.2
points below 200°K. deviate from the smooth curves by f 0.17 per cent, whereas one hundred and fifty-four points above that temperature possess an average deviation of & 0.10 per cent. The following systematic errors are considered : 1. Temperature scale. Our temperature scale is believed to be accurate to f 0.05' over the range covered. An error of 0.05' a t 296'K. would introduce an error of 0.013 per cent into determinations of the apparatus
TABLE 8 Viscosity of nitric oz'ide DATE
__-'IC.
October 6, 1937
September 21, 193 230.03 1552.7 118.95 836.2 1552.6 1552.6 836.3 835.8 836.1 245.18 1636.9 1636.5 1636,7 133.71 936.9 936.9
260.03 1723.4 1726.7 1725.1
134.55 945.4 945.4 143.051002.3 1004.0 1003.2
273.16 1793.2 1789.2 1787.6 1790.0
157.081097.3 1097.9 1097.6 September 22, 193
285.33 1856.9 1853.2 1855.0
September 21, 193
300.12 1936.8 1933.5 1933.8 1934.7
170.211183.3 1182.1 1182.7 September 21, 193
184.041270.8 1271.8 1271.3
September 22, 193 300.17 1935.1 200.86 1375.1 1375.8 1375.5 1935.4 1935.2
l l
215.72 1466.7 1468.2 1467.4
DATE
T
__
7x107
__
AVEBAQB
x 107 -
'K.
DATE
T
7x10'
-__-
AVEBAQE 7
x 1v
OK.
September 24, 1937 185.20 923.0
926.3 923.5 924.3 September 25, 1937 201.171013.1
993.4 1012.2 1006.2 215.54 1075.7 1077.4 1076.6 229.94 1150.1 1147.3 1148.7
September 25, 193: 259.97 1293.9
1295.8 1294.8 273.28 1362.6 1361.5 1361.0 1361.6 285.77 1422.2 1420.6 1421.4 300.10 1488.0 1490.2 1489.1 September 24,193; 300.15 1490.2
245.00 1217.4 1219.8 1218.6
1489.1 1489.7
TABLE 10 Viscosity OJ methane DATB
October 8, 1937 October 7, 1937
118.63 471.6 472.8 473.8 472 7
215.48
~1
1~
,
231.24
132 40 524.5 525.6 525.0 1 ;
I!
146.19 578.2 576.9 577.5
~
I
835.9 836.0
836.0
888.5 889.9
889.2
939.2 939.4
939.3
~
ii
' 260.05 985.8 987.6
183.13 722.3 714.1 714.9 717.1
!/
I
1
j 284.85 1068.5 1069.0 1068.7
I
300.00 1116.2
'I
I;
~
li
P
QAB
..
T
_-__
1116.4 1116.1 1116.2
v
x
107
mm.
OK.
154
299.93
893.4 894.0
363
299.95
895.8 893.8
561
299.93
895.3 895.6
757
299.95
895.7
79
300.05
1114.7 1114.2
448
1116.1
758
1116.2 1116.4 1050
986.7
i 273.18 1029.4 1030.6 1030.0
/Ii i
i1
Methane
775.7
157.45 619.9 I' 619.9 619.9 1 1 170.53 667.7 667.4 667.6
Hydrogen
246.10
775.9
-
1051
VISCOSITIES OF G.4SES
cwiiktuiit and a&ct all *ubieyueut measurements of viscosity by this same amount. An equal error at a temperature other than 296°K. would introducc erioib into the viwwitieq in proportion to their magnitudes and their tenipvraturc coefficients. On a percentage basis the error would be largest Tor mcthanc) a t 00"1
