23 November 1937
P h y s i c a IV~ n o 10
MEASUREMENTS O F LIQUID H E L I U M TEMPERATURES I. THE BOILING POINT OF HELIUM b y G. S C H M I D T and W. H. K E E S O M
Communication No. 250b from the Kamerlingh Onnes Laboratory at Leiden
Summary This paper deals with a new determination of the normal boiling point of helium. Use was made of a helium thermometer with reduced ice point pressure read by means of a hot wire manometer. A description of t h e apparatus is given. The helium boiling point was derived from the hydrogen boiling point. The result was 4.216~
w 1. Introduction. Liquid helium t e m p e r a t u r e s were m e a s u r e d b y m e a n s of the helium t h e r m o m e t e r in connection with v a p o u r pressure measurements by Kamerlingh Onnes in 1908: boiling point 1), in 1911 : 3-760 m m 2), and from boiling to critical point 3), b y Kamerlingh Onnes and Sophus Weber in 1915: 1.475 to 5.16~ 4 ) , a n d b y K e e s o m , Sophus Weber, Norg a a r d and S c h m i d t in 1929:0.897 to 4.22~ 5) e). The results of these m e a s u r e m e n t s h a v e been used sucessively to fix the t e m p e r a t u r e scale of the liquid helium range. I n the latest 5 years the scale 1932 7) was used, which as well as the scale 1929 was based on the m e a s u r e m e n t s of 1929. Experience in low pressure m e a s u r e m e n t s as well as knowledge of tlhe laws of rarefied gases h a v i n g m u c h a d v a n c e d since t h e n we considered t h a t t i m e h a d come to perform a new series of measurem e n t s for still b e t t e r fixing the t e m p e r a t u r e scale for the liquid helium range. F o r this purpose we aimed at obtaining with the helium t h e r m o m e t e r with reduced ice point pressure and read b y hot wire m a n o m e t e r the same a c c u r a c y as is obtained with the n o r m a l helium t h e r m o m e --
G. SCHMIDTAND W. H. KEESOM
ter at higher temperatures. Control measurements on the vapour pressure curve of hydrogen confirmed our expectation that this would be possible. In this paper the apparatus will be described and a report will be given on a new determination of the boiling point of helium. A subsequent paper will deal on the vapour pressure curve from the boiling point downwards.
w Apparatus. a. T h e h e l i u m thermometer. The apparatus is shown in fig. 1. By'means of a small gas pipette A known quantities of helium gas of a pressure of about 1 atm can be admitted to the thermometer through the narrow inlet capillary B. The slightly wider manometer capillary C has been kept very short, It ends in a hot wire manometer M (5 Wollaston wire). The manometer M forms part of a small reservoir that, being filled with liquid oxygen by condensing, serves as a bath of constant temperature. The inlet tube of this reservoir forms with the surrounding tube D a vacuum mantle which prevents untimely condensation of the oxygen during the GJ process of filling the reservoir. The whole is surrounded by a mantle space E that reaches down to the lower end 0_ ~ _N of the manometer capillary. The small upwards closed space F so formed round this capillary fills with helium vapour when liquid helium is poured into the cryostat. As a matter of fact the small heat current which flows Fig. 1. Apparatus to determine the vapour pressure curve of down through this gas column, issuing helium.
NEW MEASUREMENTS OF LIQUID HELIUM TEMPERATURES. I
from the liquid oxygen reservoir, constantly pushes, the helium meniscus in this closed space down to the lower rim G of the mantle. So a lowering of the helium level during the measurements is prevented. We remark that the arrangement of the manometer in the liquid oxygen bath prevents impurities to reach the manometer wire. Consequently the calibration performed at the beginning of a measuring day remains valid as long as the cryostat remains at low temperature. The temperatures at different points of the manometer capillary could be measured by means of three copper-constantan thermoelements Cu-Co. The thermostatic control of the liquid oxygen bath was performed as follows. While filling the cryostat with liquid hydrogen or helium a definite quantity of oxygen was condensed into the reservoir b y admitting a small quantity of helium gas into the mantle E b y means of the small pipette H. The vapour pressure Of the oxygen was controlled by means of a mercury manometer of which one leg carries a platinum contact. When the slowly decreasing vapour pressure attains the correct value, a small electric current flowing through a iheating coil laid round the reservoir is switched in. At this moment the pressure in the mantle is adjusted at a proper value to be read on the galvanometer of an auxiliary manometer (not shown in the fig.) kept at room temperature. This control once adjusted needed no correction during a whole day of the trial hydrogen measurement. With the helium measurements it proved to be necessary now and then to correct the pressure in the mantle in consequence of the helium being adsorbed at or desorbed from the walls. The Wheatstone bridge of which the manometer wire forms a branch was made further of thin constantan wire wound about the manometer tube to avoid difficulties arising from the resistances of leading wires or from thermoelectric forces. Unequal contractions of the different glass tubes were done for by the spirals P and the the rubber ring Q. T h e chief numerical data are: reservoir 39.62 cm 3 at 18~ diameter of the manometer capillary 0.0848 cm, length 9.5 cm, diameter of the inlet capillary 0.0495 cm, manometer volume 0.027 cm a, thermometer pipette 0.4855 cm 3, manometer temperature 76.5~ (liquid oxygen bath).
b. T h e v a p o u r pressure t u b e . The lower part o f t h e reservoir K of the vapour pressure tube L consists of a platinum cylinder N with copper bottom to establish good thermal contact between the helium in the cylinder and the liquid in the cryostat. To be sure that the helium in the vapour pressure tube has the same temperature as that in the thermometer reservoir the coper bottom of the vapour pressure tube has been soldered to a copper cylinder that surrounds the thermometer reservoir. The inlet is a doublewailed vacuum tube to prevent undercooling of the helium vapour in the vapour pressure tube at the level of the helium in the cryostat. The higher vapour pressures were measured with a mercury manometer, those below 0.3 cm mercury with a M a c L e o d. The capillary is sufficiently wide (0.423 cm), so that only below 0.1 cm mercury a correction for the thermomolecular pressure difference had to be applied. Heat radiation through the inlet tube was absorbed by a small blackened plate. c. By the arrangements described under a and b the following advantages were obtained: c~. an important reduction of the thermomolecular pressure differences, ~. an important reduction too of the dead space and the volume of the thermometer capillary, y. elimination of the uncertainties, arising from the descent of the liquid helium level, 8. prevention of impurities such as water vapour from the grease of the cocks to reach the manometer wire by placing the manometer in a bath of liquid oxygen (or nitrogen). w
T h e b o i l i n g p o i n t o/ h e l i u m ,
a. T h e
i n e a s u r e m e n t s.
The boiling point of helium was derived from that of hydrogen. For this purpose the cryostat on a measuring day was first filled with liquid hydrogen and then with liquid helium. The measurements were made as follows. We first measured the zero current of the hot wire manometer the thermometer being evacuated. From this moment on the thermometer pipette was constantly connected with a container (41) filled with helium at about 1 atm and kept at constant temperature. One pipette of helium was admitted to the thermometer at the hydrogen boiling point, and manometer current and vapour pressure of a small quantity
OF LIQUID HELIUM TEMPERATURES.
of liquid hydrogen in the vapour pressure tube were measured. Then the liquid hydrogen was replaced by liquid helium. At the boiling pgint the pressures in the thermometer were measured with the same filling as served for the hydrogen measurement and after admitting successively 4 times the same quantity of helium. These measurements give at the same time a calibration of the hot wire manometer and the ratio of the boiling points of hydrogen and of helium. Then followed a series of measurements of vapour pressures at lower temperatures (to be dealt with in a subsequent paper). We mention the following numerical data. The temperature of the liquid oxygen bath could after some trials be kept constant to 1 in 50000, fluctuations due to the periodical switching in of the thermostat included. The temperature excess of the Wollaston wire for balance of the bridge was about 20 degrees. The pressure could between 0.05 and 1 mm mercury be read with an accuracy of 1 to 20000. The current adjusted itself within a few seconds. Thermoelectric forces were very small and eliminated by commutation. b. R e s u 1 t s. Table I gives a survey of the calibration of the hot wire manometer for the measurements of 4 March 1937. TABLE I Manometer calibration 4 March 1937
N u m b e r of pipettes admitted
P m m Hg
Ratio of pressures
corrected (mA) ~
0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.5500 0.6000 0.6500 0.7000 0.7500 0.8000 0.8800 0.9000 0.9500 1.0000
12.062 14.537 17.008 19.469 21.917 24.356 26.779 29.184 31.575 33.958 36.329 38.695 41.054 43.403 45.746 48.079 50.406
T o t a l correc-
tion ~ +0.39 (i0* = 0.617) --0.73
2.475 2.471 2.461 2.448 2.439 2.423 2.405 2.391 2.383 2.371 2.366
2.359 2.349 2.343 2.333 2.327
Between each set of t w o experimental points three points were calculated b y interpolation.
G. S C H M I D T A N D W. H. K E E S O M
In this table S represents the pressure in the thermometer reservoir the final pressure being taken as a unit. This number is equal to the ratio of the numbers of pipettes admitted. Columns 3 and 4 form the calibration data of the manometer. Column 6 is inserted for interpolation purposes. It proved to be advantageous to correct the values of i2--i~ by the amounts given in column 5 instead of correcting the pressure ratios. Table II gives the results of the boiling point measurements. T A B L E II Boiling point of helium
Vapour pressure em Hg
Number of pipettes
i2--i~ (mA) ~
4 March 1937 1
~ Pressure ratio
T corrected ~
20.327 (20.383 )
4.218 (4.2145 )
21 April 1937
Hydrogen 1 x t/2
21 April 1937
Hydrogen 2 x 1/2 !
Iil the measurements of 21 April 1937 the quantity of helium admitted at 20.4~ was divided over two portions. So the influence of the correction for adsorptiorL at the wall could be checked. The following is an example of a list of the corrections which together give the correction mentioned in column 7.
Scheme of corrections. Measurement of 4 March 1937. Adsorption at 4.2~ . . . . . . . . . . . . . . . Reduction to A v o g a d r o scale . . . . . . . . . . . Decrease of the pressure in the pipette reservoir . . . . Change of t e m p e r a t u r e difference between pipette and pipette reservoir . . . . . . . . . . . . . . . .
+ 1.4CO/0o + 0.40 + 0.42
Thermomolecular pressure effect Dead space . . . . . . . . . . Remaining pressure in pipette . Difference of level . . . . . . .
+ 4.04~ . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . .
1.20% o 0.87 0.27 0.12 2.460/00
Total + 1.6O/oo The boiling point of h y d r o g e n 20.381~ was taken from the measurements of K e e s o m , B i j l and Miss v a n d e r H o r s t S ) and recalculated to the scale 1936 9) : ~nHe = 0.00366071, 0Ax --- 0nHea = - - 0.042, T0oc = 273.144 *). W e have given larger weights to the measurements of 21 April 1937, and take as the average result for the boiling point of helium T -----4.216~ The agreement with the result of the measurements of 1913 (4.22~ is very satisfactory.
*) I t h a s a p p e a r e d t h a t t h e r e d a c t i o n of S u p p l . No. 80a c a n give rise to s o m e unc e r t a i n t y . To e l i m i n a t e m o r e o v e r a slight d i s c r e p a n c y it m a y be s t i p u l a t e d t h a t t h e d e f i n i t i o n of S u p p l . No. 80a is t o be u n d e r s t o o d as follows. T h e A v o g a d r o scale 1936 is b a s e d o n t h e t e m p e r a t u r e coefficient eta = 0.00366107, so t h a t a b s o l u t e zeroAs s i t u a t e d a t - - 273.144~ T h e C e l s i u s - A v o g a d r o scale is realized b y a d o p t i n g ~nHe ~ 0 . 0 0 3 6 6 0 7 : for t h e f u n d a m e n t a l p r e s s u r e coefficient of h e l i u m , a n d as t a b l e of r e d u c t i o n of t h e 0.00366071 Celsius scale of t h e n o r m a l h e l i u m t h e r m o m e t e r to t h e C e l s i u s - A v o g r a d r o s c a l e t a b l e X I of C o m m u n . K a m e r l i n g h O n n e s L a b . , L e i d e n , S u p p l . No. 78 (W. H . K.).
N E W M E A S U R E M E N T S OF L I Q U I D H E L I U M T E M P E R A T U R E S . I REFERENCES
1) H. K a m e r l i n g h Onnes, Commun. K a m e r l i n g h O n n e s L a b . , L e i d e n N o . 108, w 6; Proc. roy. Acad. A m s t e r d a m 11, 168, 1908. 2) H. K a m e r l i n g h Onnes, Commun. No. 119, w 4; Proc. 13, 1093, 1911. 3) H. K a m e r l i n g h Onnes, Commun. No. 124b,w 1;Proc, 14,678, 1912. 4) H. K a m e r l i n g h Onnes and S o p h u s Weber, Commun. No.147b;Proc. 18, 493, 1915. 5) W . H . K e e s o m , Sophus WeberandG. Norgaard, Commun. No. 202b; Proe. 3-'2, 864, 1929. 6) W . H . K e e s o m , Sophus Weber andG. Schmidt, Commun. No. 202c; Proc. 32, 1314, 1929. 7) W . H . K e e s o m, Commun. Suppl. No. 71d; Rapp. Commun. 6e Congr. int. Froid, Buenos Aires, No. 4, 1932. 8) W . H . K e e s o m , A. B i j l a n d M i s s H , v a n d e r H o r s ' t , Commun. No. 217a; Proc. 34, 1223, 1931. 9) "~u H. K e e s o m, Commun. Suppl. No. 80a; Rapp. Commun. 7e Congr. iat. Froid, La H a y e - A m s t e r d a m , No. 5, 1935.