- Email: [email protected]
The vapour pressure of liquid oxygen
Muijlwijk, Van
Physica
R.
Moussa,
Dijk,
32
805-822
M. 1~. H.
1966
THE VAPOUR
PRESSURE
by R. MUIJLWIJK, Communication
OF LIQUID
M. R. MOUSSA”)
No. 346~ from the Kamerlingh
OXYGEN
and H. VAN
Onnes Laboratorium,
DIJK
Leiden,
Nederland
Synopsis From
a thermodynamic
saturated
vapour
information. of the
apparatuses. from
compared
temperatures by a smooth The triple
pressure
thermometers
PRMI
KPL
the platinum
Fig. 5 shows
carried
were previously
and
oxygen out
p-T
thermometer
and
in two
calibrated
respectively.
that their difference
of the
experimental
of liquid
were
using the thermodynamic from
of the pressure
available
on the
Temperatures relation
were
readings.
The
can be represented
curve. point
at the triple point 54.350”K.
derived
using
of the vapour
thermometers
PSU,
measurements equal.
dependence
calculated
of platinum
of NBS,
temperatures
are nearly
was
measurements
The platinum
scales
the pressure
with
the temperature
oxygen
of a number
gas thermometer derived
equation
liquid
Simultaneous
resistance
different
of
of oxygen
was also measured.
We
1.0975 mm Hg at 0°C and standard
A formula
for the P-T
relation
of oxygen
found gravity
for the vapour
pressure
and for the temperature
is proposed
and a table has been
calculated.
The relation between the vapour pressure of liquid 1. Introduction. oxygen and temperature (p--T relation) can be obtained from measurements of p and T, and from thermodynamic calculations. The accuracy of the result obtained from measurements of p and T is mainly limited by the inaccuracies of the gas thermometric measurements.The use of a thermodynamic P-T relation helps us to avoid or to eliminate irregularities contained in the gas thermometric results. The accuracy of the thermodynamic P-T relation is limited by the accuracy of the data for thermodynamic quantities, which are used in the calculations. An accurate p-T relation was obtained by representing our results obtained from p and T measurements in an equation, that satisfies the requirements of thermodynamics within the limits of the available experimental data. The study of the p--T relation for liquid oxygen is of interest in several respects. a. This relation is used in thermometry to derive temperatures from measured vapour pressures. b. If the p-T relation is known accurately temperature scales, which are *) Mission member
of the National
Research
-
Centre of Egypt.
805
-
806
R. MUIJLWIJK,
based on the thermometers, a function calculations
of the
P-T
with the P-T
An accurate
H. VAN
knowledge
DIJK
calibrated the vapour
against gas pressure as
on such a scale.
of fi and T is an excellent
a.
AND
use of platinum thermometers can be checked by measuring
of temperature
A comparison
C.
M. R. MOUSSA
relation
relation
obtained
obtained
from
thermodynamic
from direct measurements
way to check the consistency
of both results.
of the vapour pressure-temperature
relation
of
liquid oxygen enables us to calibrate secundary thermometers (usually platinum thermometers) accurately between 54 and 100°K. In this paper a thermodynamic P-T relation for the saturated vapour of liquid oxygen and for temperatures between 54 and 100°K is given and discussed in section 2. A description of our apparatus is given in section 3. In section 4 the experiments and the method used to convert the experimental data in temperatures are described. In section 5 the experimental results are given. In section 6 our results are discussed and represented in a formula. 2. The thermodynamic p-T relation. a. Introduction. It can be shown from thermodynamicsi) that the vapour pressure-temperature relation for the saturated vapour of liquid oxygen can be written as: ln@/pi)
= A(1 -
In this equation The heat due T =
Tr/T) + ln(T/Ti)
+ 11 -
1s + 1s + 8 -
pi is the vapour pressure at a reference
~1.
temperature
(1) T1
constant A is equal to L(Tl)/RTl - 1 - 71, where L(Tl) is the molar of vaporization at T1 and R the gas constant. E and r] are corrections to the non-ideality of the gas, ~1 and 71 are the values of E and q for T1. II = ;(C,
-
C.,)/RT
dT
1’1 1s
=
(l/RT) /‘CC, -
Cvt) dT
Tl
I3 = (1 /RT) J%n(dp/dT)
dT;
T1
CL and Vn are respectively, the molar heat capacity and the molar volume of the liquid, C,, is the molar heat capacity of the gas at such a large molar volume, Vi, that the gas can be treated as an ideal gas. For liquid oxygen, C,, = #R. All terms in eq. (1) can be computed today with a reasonable precision for temperatures between 100°K and 54.35”K using available experimental information. The data needed to compute the vapour pressure b. Computations. of oxygen using eq. (1) have been gathered and discussed by Mullins,
THE VAPOIJR
I
+20
-10
t
T
1. Temperature according
.
I
I
70
equivalent
to different
of
I I
the
differences
OK
90
in
vapour
calculations.
TABLE
I (00
I
I
80
thermodynamic
807
OXYGEN
I
60
1
OF LIQUID
I
I
50
pig.
PRESSURE
pressure
Explanation
of
oxygen
in the text.
I
Abstract of the evaluation of the thermodynamicvapour pressure-temperature relation for liquid oxygen T
“K
Ziegler
and
Kirk
temperatures and pressure matical
they
result
Institute
They
calculated
100 and 54.352 T1 =
E -
P mm Hg at 09
El
1.344 5.459 17.554 47.073 109.354 226.437 427.149 746.584 1225.224 1908.022
- 0.03064 -0.03018 -0.02912 - 0.02707 -0.02359 -0.01822 -0.01059 -0,00039 +0.01258 - + 0.02846
90.168”K
“K.
the vapour
For
0.3080 + 0.2549 +0.2140 +0.1818 +0.1562 $0.1356 +0.1188 +0.1050 + 0.0935 + 0.0839 +
assistant
Using
at the Mathe-
essentially
the same representation
the same
of these data,
at 91 = 760 mm Hg at 0°C he got very nearly
differences An abstract
for
equal
fig. 1 where
pressures
of the main
at 25
temperature
at $1 = 760 mm Hg at 0°C. These
of Leiden.
This can be seen from
1 In P/dT “K-1
pressure
the reference
for us by Mr. W. Nuy,
of the University
90.170”K
temperature table
used
B liter mole-l -0.54949 -0.46496 - 0.40069 - 0.35031 - 0.30981 - 0.27660 - 0.24890 - 0.22545 -0.20536 - 0.18796
data and very nearly
as MZK.
and MZK.
-0.00602 - 0.00549 - 0.00499 - 0.00446 -0.00381 -0.00295 -0.00174 - 0.00007 + 0.00223 + 0.00529
were repeated
thermodynamic but T1 =
13
(MZK)2).
between
calculations
-
VL cm3 mole-’ +24.771 +25.156 + 25.562 + 25.993 + 26.450 + 26.938 +27.461 + 28.024 + 28.635 +29.300
I1 - 1%
results
curve
between
the same
A represents
the
results
of the calculations
the
of Nuy
is given
in
I.
To calculate Lennard-
Jones
e/k = 112°K
the second
virial
6-l 2 potential and
bo =
coefficient
function
for the vapour,
characterized
60.84 cm3 mole- 1. Different
MZK
used
a
by the two parameters values
for these
para-
808
R. MUIJLWIJK,
M. R. MOUSSA
meters were given by Hirschfeldera) Hirschfelder and Benedict
AND
H. VAN
DIJK
and by Woolley
-_____.
and BenedictJ).
gives e/k = 118 “K and bo = 52.25 cmsmole-1. give e/k = 116 “K and bo = 54.7 cmsmole-1.
MZK chose the parameters
in such a way that they obtained
Woolley agreement
with the $--T data of Hoge. Nuy
duplicated
and bo instead
his computation
of the MZK values.
using
Hirschfelder’s
data
for e/k
Curve B in fig. 1 shows the differences
between the first and the second computation of Nuy. The difference at 54 “K is about 16 m”K. To estimate the total uncertainty in the p-T relation calculated in this way, the uncertainties arising from possible errors in L(T), CL and Vn have to be added. The uncertainties due to uncertainties in CL and Vn are small and very small. The influence of the uncertainties can be reduced if we know the pressures (pi and Pz) of the saturated vapour; at two temperatures (T1 and Tz) sufficiently accurately. The constant A can then be eliminated from eq. (1) and the equation can be written: TZ T2 -
Ti
ln p-C(T2,TlJ}(1 PJ1
-l)iln$-
CCT,Td
P1T2
where C(T, TI) = Il(T, Tl) - Is(T, TI) + Is(T, T1) + E - cl. The coefficient of [l - (Tl/T)] in eq. (2) is slightly depending on the values chosen for e/k and bo, but equation (2) will always give pi at T1 and ps at Ts. When the results of Nuy’s first and second computation were made to agree at the boiling point and near the triple point of 0s by changing the coefficient A a little, the maximum difference in temperature for equal pressure reduced to only 6 m”K. The temperature dependence of this difference is shown in fig. 1 curve C. The changes in A that we need to reconcile the results of both computations and our experimental data for p and T at the triple point are smaller than 0.1 y0 and are well within the uncertainty of the experimental data available to calculate A. 3. Afiparahs. The vapour pressure-temperature relation for the saturated vapour of liquid oxygen was measured at many temperatures from 96 to 54.35”K. The temperature was measured with resistance thermometers which were calibrated on the NBS, PSU, PRMI or NPL gas thermometer scales below 90 “K. The vapour pressure was measured above 5 cm Hg with a mercury manometer and below 5 cm Hg with an oil manometer. Two different apparatuses were used. In the first apparatus, A (see fig. 2), four platinum thermometers were placed in holes in a copper block which was suspended in a metal can. Usually approximately 8 cm3 of liquid oxygen was condensed in this can so that the block was partly immersed. The inner can was separated from the surrounding oxygen bath by a jacket in which gas could be admitted. By changing the pressure of the gas the
THE
VAPOUR
1
PRESSURE
OF LIQUID
809
OXYGEN
1
86
80
k-40-q
r -7 C
I-z4
46
Fig. 2a.
Apparatus
A.
Fig.
2b.
Apparatus
B.
810 heat contact The jacket
K.
MUIJLWIJK,
between surrounded
M. Ii. MOUSSA
In this apparatus of Standards
DIJK
bath could be varied.
also the lower part of the capillary, to avoid condensation
there was a radiation
in the capillary.
were used:
No. 113760 1 (LN), calibrated
in Washington
which connected
shield.
the following thermometers
Leeds and Northrup
H. VAN
the inner can and the oxygen
the inner can with the manometers, Below the capillary
AND
on the NBS-1955
at the National Bureau
scale,
Tinsley No. 153371 (NPL 1) calibrated at the National Physical Laboratory in Teddington on the NPL scale, T 4, calibrated at the Physico-Technical and Radio-Technical Measurements Institute in Moscow on the PRMI scale, KOL 143, constructed in our laboratory and compared previously with LN No. 1137601. This apparatus was also used to measure the triple point pressure and temperature. The second apparatus, B (see fig. 2), consisted of a copper block in which 8 thermometers were inserted in holes around a central cavity. In this central cavity oxygen gas could be condensed through a capillary, connecting the cavity with the manometer system. The capillary was surrounded by a jacket, which was usually evacuated. There was a radiation shield inside the capillary just above the block. The copper block was surrounded by a not entirely closed copper shield fixed to the top of the block. This shield served to reduce vertical temperature gradients in the block, which are caused by the hydrostatic pressure differences in the bath. This apparatus was not suitable for triple point measurements, but the replacement of thermometers was much easier than in apparatus A. The thermometers used in this apparatus were: State University on PSU 1577534 (PSU 4), calibrated at the Pennsylvania the PSU scale calibrated at PRMI on the PRMI scale. T 4, NBS 1575702 (NBS 2), calibrated calibrated Tinsley 164956 (B 2)) PSU 1577533 (PSU 3), calibrated calibrated T 2, calibrated LN 1137601 (LN), NPL 153373 (NPL 3), calibrated
at at at at at at
NBS NPL PSU PRMI NBS NPL
on the NBS- 1955 scale on the NPL scale on the PSU scale on the PRMI scale on the NBS-1955 scale on the NPL scale.
The thermometers PSU 3, PSU 4, NBS 2, T 2 and NPL 3 were used previously for the international comparison of the 4 scales mentioned above at NPL5) and at PRMIS). The thermometers T 4 and LN were also used were made with these two in apparatus A, most of our measurements thermometers. The data for the thermometers KOL 143 and B 2 will not with be given here. In these two pieces of apparatus also measurements nitrogen 7), hydrogens) and helium were carried out.
THE
VAPOUR
PRESSURE
OF LIQUID
811
OXYGEN
The experiments consisted in simultaneous measurements 4. Ex$eriments. of the vapour pressure of oxygen and of the resistance of platinum thermometers. Temperatures were derived from the measured vapour pressures using a table calculated by N uy. This table gives the pressures and pressure differences in steps of O.l”K between 54 and 100°K. The data of the table are calculated with the equation: r”log fi = 28.888394 -
10.5434702 lolog T + 0.01934976 T + -
1880.776
666.13713 +
T
(3)
T2
where fi is expressed in mm Hg at 0°C and standard gravity and T in “K. This equation represents the 25 fi-T data of MZK for temperatures from
Fig. 3 50
1
50
T
60
70
80
70
5.0
90
OK
100
300
250
200
106,w I 150 ,60
90
OK
100
Fig. 4
Fig. 3 and 4. Differences in W = (R/2&,) between thermometers as obtained from our measurements compared with the averaged result from the measurements at NPL and at PRMI. 0 02 measurements q Nz measurements
812
MUIJLWIJK,
Ii.
Ill. K. MOUSSA
54.35 to 100°K with a standard
deviation
AND
H. VAN
DIJK
of only 0.14 m”K and a maximum
deviation of 0.27 m”K. To obtain temperatures according to Nuy’s first thermodynamic calculation mentioned in section 2 a graph was used. The graph between
shows the
the differences
result
of Nuy’s
and the calculation
in temperature
first
for equal
thermodynamic
with eq. (3). This graph
pressure
calculation
gives curve
with
values eq. (1)
A of fig. 1 on a large
scale. Temperatures
according
to Nuy’s
first thermodynamic
calculations
with
eq. (1) were denoted T,. From the reduced resistance W = K(T)/R (O’C), of the thermometers temperatures were derived on the RI scale. The BI scale is a smoothed average of four gas thermometer scales (NBS, PSU, NPL and PRMI scale). It is obtained from the rtlsult of the intercomparison of scales at NPL5) and PRMIa) and is described briefly in the appendix of our paper on the vapour pressure of nitrogen’). For the data near the boiling point and at the triple point, temperatures were derived also on the NBS, PSU, NPL and PRMI scale and on the reduced scales (see section 6 and the appendix mentioned above). The trmpcrature drift during the experiments was nearly always between 1 and 0.5 m “K per minute. The accuracy of the resistance measurements can be estimated from fig. 3 and 4. In these figures the differences in W between different thermometers are given together with a smooth average of these differences as reported by NPL and PRMI. The equivalent of 1 m “K is in the whole temperature range approximately 4 x 1OW in IV. 5. Experivaental results. a. Temperature 96 “K. The measured pressures and temperatures
50
Fig. 5. Differences thermometers
--
T
60
between
and expressed 0
80
70
temperatures
deduced
range between 54.35 and and the differences between
90
OK
from measurements
100
with platinum
on the HI scale and temperatures, T,, deduced pressure measurements. Apparatus I3 0 Apparatus .4
from vapour
THE
VAPOUR
PRESSURE
OF LIQUID
TABLE Differences thermometer -
between
the temperatures
measurements
pressure measurements.
II
on the BI scale deduced
and temperatures,
(The meaning
813
OXYGEN
T,,
of w is explained
Apparatus
from platinum
deduced
from
in section
vapour 6)
A
28. a.363
18.469
65.2386
136373
47.997
70.1071
157032
65.2462 70.1157
7.6
29. 8.‘63
8.6
29. a.‘63
225.34
79.9643
199539
79.9759
11.6
29. a.‘63
431.07
85.0768
221728
85.0881
11.3
29. 8.‘63
780.57
90.4262
244940
90.4328
6.6
2. 9.‘63
773.93
90.3446
244590
90.3522
7.6
2. 9.‘63
771.37
90.3123
244450
90.3199
7.6
54.3476
91959
54.3496
2.0
15.10.‘63
178.05
78.2696
192194
78.2807
11.1
15.10.‘63
345.08
83.2445
213774
83.2565
12.0
15.10.‘63
620.90
88.2801
235635
88.2899
9.8
130746
63.9046
6.5
24. 9.‘63
16.10.‘63
1.0975
13.804
63.898
85.495
I
73.460 1
171435
73.4734
29.
1.‘64
234.51
80.259 1
200820
80.2713
13.3 12.2
29.
1.‘64
296.46
82.0423
208552
82.0536
11.3
29.
1.‘64
476.76
85.9357
225453
85.9458
10.1
29.
1.‘64
599.71
87.9642
234258
87.9729
a.7
29.
1.‘64
748.57
243203
90.0327
7.3
30.
1.‘64
768.18
90.0254 90.2724
244283
90.2815
9.1
30.
1.‘64
664.92
88.91 IO
23837 1
88.9199
8.9
63.1051
127437
63.1118
6.7
2443 18
90.2895
a.6
16.10.‘63
24. 3.‘64
11.546
25. 3.‘64
768.86
90.2809
12. 5.‘64
70.5487
t 58929
70.5599
11.2
13. 5.‘64
51.97 771.14
90.3093
244442
90.3181
8.8
13. 5.‘64
771.52
90.3143
244458
90.3220
14. 5.‘64
344.79
83.2378
213733
83.247
14. 5.‘64
233.10
80.2140
200615
80.2240
10.0
14. 5.‘64
117.52
75.4638 62.1447
i 80045
75.4709
7.1
123440
62.1499
5.2
114355
59.9440
9.1
244425
6.1
Apparatus
B
26. 5.‘64
9.238
26. 5.‘64
59.9349
28. 5.‘64 28. 5’64
5.369 771.03 928.38
92.1287
252340
90.3142 92.1377
28. 5.‘64
1123.64
94.0841
260809
94.09’01
29. 5.‘64
1356.80
96.1043
269556
90.308
-
i
-
96.1083
7.7
i
9.3
9.0 6.0
-
4.0
values and the corresponding TBI values are given in table II and shown fig. 5. A smooth curve, showing no irregularities, yas drawn through the experimental points in fig. 5. This curve deviates nowhere more than 11 m”K from the zero line. The difference of 8 m “K at the boiling point is caused for 3 m”K by the differences between the BI scale and the average reduced scale (see fig. 6) and for 5 m”K by the fact that our realization of the boiling point temperature is 5 m”K different from the average result obtained at T,
in
814
K.
MUIJLWIJK,
SO&
M. R. MOUSSA
60
Fig. 6. Differences
70
between
AND
H. VAN
80
DIJK
OK
90
the BI scale and the average
reduced
100
scale.
the four other institutes. We will discuss this point in more detail in the sections 5b and 6. b. The boiling point. From the measurements near to the boiling point the resistance ratio R/R,,, was calculated at the boiling point. From these resistance ratio’s the temperatures T, were calculated. T, is the temperature on the scale on which each thermometer was calibrated (NPL, NBS-1955, PRMI or PSU scale). The results are given in table III. T,, denotes the temperature on each scale when it is reduced to the agreed values of the boiling points of oxygen and normal hydrogen (90.170”K and 20.384 “K respectively). TABLE Values obtained
for the boiling point of oxygen calibrated
r Thermometer
LN
1137601
III
at 4 different
Apparatus
A
with thermometers
institutes
I
Apparatus
B
Tn
‘Tnr
Tn
“K
“K
“K
OK
90.1857
90.1757
90.1813
90.1713
TW
NBS
1575702
90.1825
90.1725
PSU
1577533
90.1572
90.1762
PSU
1577534
90.1563
90.1753
NPL
153371
90.1046 90.2064
90.1746 90.1774
90.2075
90.1785
NPL
153373
PRMI
4
PRMI
2
90.1811
90.1711
90.2062
90.1772
The obtained reduced temperatures are 2-8 m”K higher than 90.170”K. The highest values were found for the PRMI thermometers. In the ideal case, that no errors were made in the determinations of the boiling point on each of the four scales and in the calibration of the thermometers on these scales, at each of the four institutes, and that there is no error in our measurements and no change in the calibration of the thermometers, T,, would be equal to 90.170”K. Our data for the boiling point of oxygen obtained from measurements near the boiling point with thermometers of the international group are compared in table IV with results obtained at NPL and PRMI. The 1963 data are deduced by means of interpolation from the comparison data communicated by Barber and Orlova to the members of the working
81:
THE VAPOUR PRESSURE OF LIQUID OXYGEN TABLE IV Comparison of thermometers 153372 243764.!
NPL 1963
of the international
-
-
NPL
90.179’ 90.169’
NPL NBS 153373 1575702 7 5 243767.8 243937.8 7 90.1803 90.1784”) 7 90.1703 90.1684 243758.7 243924.4 90.i 782 90.1753;) 7 90.1682 90.1653
243760.’ 7
PRMI 1963
group at the boiling point of oxygen
-
NBS
PRMI
PSU
T2
T3
1577533
1577: 24401
PSl
243697.5
;243706.2
244010.3
90.17918)
90.2007
90.2027
90.1523
90.1
90.1691
90.1717
90.1737
90.1713
90.1
243940.8
243957.7
243690.5
244002.1
24401
90. I 78’ ?
90.1770*)
90.1990
90.1504
90.1.
90.168’
90.1670
90.1700
90.1694
90.1
243757 243934 90.1778 90.1775*) 90.1681 3 90.1678 90.1675 90.1781 3
243786 243955 90.1846 90.1825*) 90.1746 90.1725
KOL 1964
90.1520
90.11
90.1702
90.1710
90.1’
244032
24403
90.2075
90.1572
90.11
90.1785
90.1762
90.1’
25.5359
25.5
25.5359
25.5
25.0894
-
24401
90.1992
243725
24.9830 25.5597 24.9831 25.5600 -
-
244009
24369 1
243757
PRMI 1964
PRMI
1575705
25.0895
-
*) NBS-1955scale **) RO before resp. after our measurements groups of the Comite Consultatif des Poids
et Mesures
by 0 rlova
de ThermomCtrie
(C.C.T.)
in 1963. The
to the same groups
at the Bureau Internationa
1964 data were communicated
in 1964. The
reduced
given in table IV differ always from 90.170 “K except they
are 90.170 by
90.170”K
temperatures
at the different
can be obtained
The boiling
main
institutes.
Average
values
at slightly
with
the PRMI
thermometer
of the results obtained
oxygen
with T2
with T4 and taken from the data mentioned This other thermometer
of PRMI
was calibrated
T2.
of the dT
only in two cases slightly The
data
differences
of table between
PRMI.
thermometer
the value 90.1773 obtained
in table III
is used in table V
in Moscow at the same time as in our laboratory.
values of table V from their average
values are
larger than 1 m”K.
V can be used to calculate the boiling
at the four other institutes. value
the value 90.1782 This
as in the liquid hydrogen
T2 and proved to be very stable during many measurements The deviations
frorr
different
for these difterence:
of table IV are used in table V except
at K.O.L. Instead
for the deviations
point was realized
gave too high values as well in the liquid region.
reason
Tnr
from the data given in table IV in the way shown in tabh
V. All data for T,, obtained
definition.
is, that the oxygen
temperatures,
in the few cases when
point temperatures
average realized
We can start this calculation
104 AT = 43 for KOL-NPL
as with the value
values
for the
at K.O.L.
and
as well with the
104 dT’=
61 for KOL-
The results are given in the columns a and b of table VI.
Column L
816
R. MUIJLWIJK,
M. R. MOUSSA
TABLE Average
values for the boiling point of oxygen
1
/
NPL
Measured NPL
/1.;:27 Tnr (AT 1 27 x
1041j .600[ Tnr
lo4 AT KOL-NPL KOL
at
PRMI
46
boiling
1 27
104 Al
1
PSU
-15 x 10411.;;15 ?‘nr
/IdT
-
1 12
the
4 Institutes
1
.i?
37
/ .1758 /
64
1
NBS
27 x 10411.k T”r
43
I.1746 I
between
points
46
I.17731
DIJK
V
I
jm
H. VAN
on the reduced scales and differences
realized pt’s from +
AND
1 33
49
-
43 _____
1.1725 1
.17505
57
61
KOL-PRMI PRMI 104m
I1;;.1701 I
19
I.16821
(
NPLPRMI
I27
/.1709/
PSU-
24
NPL
!l
I.16681
-18
.1690
’
NBSPSU
34
Differences boiling
TABLE Average
differences
points
VI
of the boiling
realized
of
realized
point
at different
temperatures
of oxygen
institutes
_-
(TKoL-TN).~@
I
h
1 L
37
46
/ (a + b +
(?‘KOL -
?‘NPL). 104
a 43
(7.~01, -
TPRMI). lo4
67
61
73
67
(TKOL -
TPSU)’
61
55
58
58
lo4
(TKOL. -
TNRS) IO4
(TKOL -
T,).
lo4
L)/3
42
27
21
25
24
495
435
505
48
gives the Leiden result, column (a + b + L)/3 gives the average of the columns a, b and L. The agreement of the results deduced from data obtained at different institutes is satisfactory. The boiling point realized at KOL is a little over 2 m”K higher than that realized at NBS, 4 m”K higher than that realized at NPL, about 6 m”K higher than that realized at PSU and about 7 m “K higher than that realized at PRMI. It is nearly 5 m”K higher than the average of the boiling points realized at the four other institutes. A lower boiling point will be realized when the oxygen contains some nitrogen. According to our experience oxygen obtained from potassium permanganate can be freed sufficiently from nitrogen by rectification. We prefer, however, to prepare our oxygen from the purest air free water by electrolysis and to free the oxygen from remainders of water and hydrogen by freezing and by fractionated distillation. c. The triple point. The triple point pressure and the triple point temperature were measured with apparatus A, by allowing the inner can to warm up slowly through the triple point. The pressure was measured with an oil manometer. The density of the Octoil-S used in the manometer was 0.9105 g cm-3 at 25°C. The cubic expansion coefficient was determined
THE
VAPOUR
between 19°C and 35°C
PRESSURE
OF LIQUID
817
OXYGEN
it was found to be 7.8 x 10-4°C-1.
Octoil-S and a high precision cathetometer
The use of the
enabled us to measure the vapour
pressure at the triple point with high accuracy. The result was ptr = 1.0975 mm Hg The temperature
at
0°C.
of the triple point was measured directly with the platinum
resistance thermometer LN 1137601. But because this thermometer was compared in the near vicinity of the triple point with the thermometers NPL 153371 and T4, the temperature of the triple point could be calculated from measurements on each of the 3 thermometers. The result is given in table VII. This result can be compared with results obtained by Hogeg) TABLE Temperature
of the triple point of oxygen
VII determined
with different
thermometers
(F., 1137601
54.3493
NPL
153371
54.3612
PRMI
T4
54.3616
LN
and by Orlovaie). Hoge’s triple point temperature on the NBS1939scale is 54.363”K, which corresponds to 54.353”K on the average reduced scale, reported the value 54.368”K. This corresponds to 54.356”K FIU. Orlova on the average reduced scale. Hoge’s result for the pressure of the saturated vapour at the triple point was fi = 1.14 mm Hg at 0°C. But since he also measured the values 1.12 and 1.13 mm Hg at 0°C the accuracy of his pressure measurements was apparantly not better than 0.02 mm Hg. 6. Disczlssion. and refiresentation of the results. four institutes NBS, PRMI, NPL and PSU thermometers
The individual scales of the are defined with standard
kept at the institute. Each institute compared
his (primary)
standard(s) with a gas thermometer at the institute and measured the temperature of boiling points of oxygen and hydrogen with its primary standard(s). The results obtained at the different institutes differ from each other as is shown in table VIII. These values differ for two reasons. TABLE The boiling
points of oxygen
and hydrogen
according CCT 1962 OK
VIII as recommended
to the different
NBS-1939 “K
individual NPL “K
by the CCT in 1962 and scales PRMI “K
PSU “K
02
90.170
90.190
90.180
90.199
90.151
n-Hz
20.384
20.3925
20.3875
20.394
20.365
818
R. MUIJLWIJK,
The main reason is, that different boiling
gas thermometric points
M. R. MOUSSA
different
H. VAN
DIJK
results have been obtained
measurements.
were not realized
AND
The second reason
at accurately
the
from the
is, that
the
same temperatures
in
the different atures,
institutes. To obtain a single generally acceptable scale temperon the individual scales were reduced with the aid of linear Tn,
reduction formulae to temperatures, T nr, on the reduced scales in such a way, that the declaredvalue for the normal oxygen boiling point becomes90.1700”K on its own reduced scale and the normal boiling point of normal hydrogen becomes 20.384”K. The scales reduced in this way are closer to each other but are not identic, not even at the boiling points. The differences between the individual reduced scales were measured at many temperatures by comparing thermometers calibrated at the four institutes. The results were confirmed by measurements at our institute. The comparisons enable to reduce the different scales to each other and also to their average, the average reduced scale (T,,), or to a proper continuous representation of it, as calculated by Orlova and othersii), the BI scale. The different values for Tnr at the boiling point of oxygen are shown in table V. We may conclude from this table, that, although T,, at the boiling point is 90.1700 on the individual reduced scales of the institutes NPL and PRMI, and is taken also 90.1700 for the boiling point realized at KOL, nevertheless the T,, values obtained from measurements on thermometers calibrated at other institutes differ from 90.1700”K. We may also conclude, that Tnr is 90. 17075 for the boiling point realized at NPL, is 90.1690 for the boiling point realized at PRMI and is 90.17505”K for the boiling point realized at KOL. Temperatures on the BI scale are at the boiling point of oxygen 2.7 m”K higher than temperatures on the average reduced scale (see fig. 6). The temperature of the normal boiling point of oxygen is therefore according to our recent measurements 90.1777 “K on the BI scale. This result is in close agreement with Barber’s result (90.182”K) obtained recently with the gas thermometer at NPLrs). Since the BI table is between 90.2 and 20°K a very good, well smoothed and well defined representation of the temperature dependence of a proper average*) of the reduced resistances of the platinum thermometers of the international group, and it was recommended for provisional use by the CCT in 1964, we compared our temperatures obtained from vapour pressure measurements with temperatures on the BI scale. According to table II deduced from vapour pressure measurements and fig. 5 temperatures T,, using Nuy’s first thermodynamic calculation and temperatures TBI, deduced from resistance measurements and expressed in the BI scale differ at the *) w = c4 FvPRMI2 + 2 WNPL’Z + 2 wNPL3 T,, = pn + 0.001952 - 0.0001325 T with
t- 2 WNBS2
+ WpSu3
+ FvpsuI)
j12;
Tn = (2 TPRMIZ + TNPL 2 + TNPL 3 + 2 TNBS~ + TPSU~ + TPSU 4) Ia, where for TNBS the NBS-1939 scale is used and NPL 2 refers to the NPL thermometer 153372.
819
THE VAPOUR PRESSURE OF LIQUID OXYGEN
boiling point nearly 8 m”K and at the triple point 2 m”K. A maximum difference of about 11 to 12 m”K was found at about 80 “K. These differences can be reduced considerably by using in the thermodynamic calculations the same value for the boiling point of oxygen as was obtained for it on the BI scale (90.1777”K). Still better agreement can be obtained by using for the calculation formula (2) and substituting for fis the accurately measured value for the vapour pressure at the triple point of oxygen (1.097jmm Hg at 0%) and for Ts the temperature of the triple point expressed on the BI scale (54.3496”K). Doing so the deviations at both fixed points become zero and the maximum deviation between both reduces to about 7 m”K. This maximum deviation is about the same as the remaining total inaccuracy in the thermodynamic calculations of the P-T relation. The deviation can be nearly reduced to zero by changing the constants used in the calculation of the virial corrections within the limits of the accuracy of the available data. In fact we used a slightly different method. Starting with eq. (3) we changed the coefficients of this equation a little in such a way, that at the boiling point and at the triple point temperatures the correct values for the vapour pressure were obtained and the average deviation for all measured temperatures became smaller than 0.2 m”K. We obtained the equation 10.534702 lolog T + 0.01932948 T +
r”log fi = 28.901847 -
667.85576
-
1937.538
T
$-
T2
(41
where fi is expressed in mm Hg at 0°C and standard gravity and T in “K. Fig. 7 shows the temperature equivalent of differences between our measured vapour pressures and vapour pressures calculated with eq. (4) from our measured temperatures expressed on the BI temperature scale. +5
o
m°K
0 0 0
0
0
000 I7
g-,““, “LO
+I
O
O
b
? tii c I -5 50
T
-60
70
80
90
OK
100
Fig. 7. Differences between temperatures on the BI scale and temperatures obtained using the revised P-T relation deduced from our measurements on platinum thermometers
and from
vapour
pressure
measurements.
Table IX gives the vapour pressure of liquid oxygen in mm Hg (OOC, standard gravity) according to eq. (4) at every tenth of a degree from 54°K up to 100°K and the differences between successive steps.
820
R. MUIJLWIJK,
M. R. MOUSSA
AND
H. VAN
DIJK
TABLE Vapour
-
.O
“K
I
.l
pressure
.2
of liquid
oxygen
i
I
c.f. eq. (4)
.3
.4
1.0804
.0347
1.1151
.0356
1.4733
.0454
1.5187
.0466
.0573
1.9853
.0588
2.0442
.0603
.0736
2.6454
.0754
2.7208
.0773
3.3940
.0935
3.4875
.0957
3.5832
.0980
.1150
4.4338
.1176
4.5514
.1203
4.6717
.1230
5.5930
.1435
5.7365
.1467
5.8832
.1499
6.033 1
.1531
7.1768
.1776
7.3544
.1813
7.5357
.1851
7.7209
8.9153
.1739 .2136
9.1290
.2180
.2224
9.5693
.2269
9.7962
.1890 .2314
63
11.2556
.2603
.2654
.2706
12.0520
.2758
12.3279
.2812
64
14.0978
.3149
11.5160 14.4127
9.3469 11.7814
.3208
14.7336
.3269
15.0604
.3330
15.3934
.3392
65
17.5245
.3783
17.9028
.3a51
18.2879
.3921
18.6800
.3991
19.0792
.4063
66
21.6277
.4513
22.0790
.4592
22.5383
.4672
23.0055
.4753
23.4808
.4a35
67
26.5089
.5351
27.0440
.5441
27.5881
.5532
28.1413
.5625
28.7038
.5718
68
32.2794
.6306
32.9100
.6408
33.5508
.6512
34.2020
.6617
34.8636
.6723
69
39.0612
.7388
.7504
41.3124
.7739
42.0863
.7859
46.9864
.8608
.8738
40.5503 48.7210
.7621
70 71
39.8000 47.8472
.8870
49.6080
.9003
50.5083
.9138
56.1981
57.1959
1.0123
58.2082
.0270
59.2353
1.0419
60.2772
1.0570
72
66.8504
.9978 1.1507
68.0012
1.1669
69.1681
.1833
70.3514
1.1999
71.5513
1.2166
73
79.1084
1.3208
80.4292
1.3388
81.7680
.3570
83.1250
1.3753
84.5003
1.3939
74
93.1483
1.5091
97.7355
1.5693
99.3049
1.5898
1.7168
1.5290 1.7387
1.549 1
109.1576
94.6575 110.8744
96.1 a65
75
112.6131
1.7607
114.3738
1.7830
116.1569
1.8055
76 77
127.3349
1.9449 2.1947
129.2798
1.9689
131.2487
1.9931
133.2418
2.0175
135.2594
2.0422
150.0844
2.2209
152.3052
2.2473
154.5525
2.2739
156.8264
2.3008
2.4670
173.5098
2.4956
176.0054
2.5243
178.5297
2.5533
181.0830
2.5826
54 1.4291
.0442
.0559
1.9280
.0718
2.5718
3.3027
.0913
.1124
4.3188
5.4525
.1404
61
7.0029
62
55
1.344 1
.0419
56 57
1.8176 2.4299
58
.043 1
.0545
1.3861 1.8721
.0701
2.5000
3.2135
.0892
59
4.2063
60
78
147.8897 171.0428
79
197.026
2.763
199.789
2.794
202.583
2.825
205.408
2.857
208.265
2.888
80
226.080
3.084
229.164
3.118
232.282
3.151
235.433
3.185
238.619
3.220
a1
258.459 294.426
3.431
261.890
3.467
265.357
3.503
268.861
3.540
272.401
3.577
3.804
298.230
3.843
302.073
3.882
305.956
3.922
309.878
3.96 1
82 83 84
334.252
4.206
338.458
4.247
342.705
4.289
346.995
4.332
351.326
4.374
378.220
4.636
382.856
387.537
4.725
392.262
4.771
397.033
85
426.623
5.096
431.718
4.680 5.143
436.862
5.191
442.053
5.239
447.292
4.816 5.288
86
479.760
5.586
496.670
5.739
502.410
6.108
490.983 550.2 11
5.688
537.941
485.346 544.049
5.637
87
556.426
6.270
562.697
5.791 6.325
88
601.484
6.662
608.146
6.719
/614.865
6.216 6.776
621.641
6.834
628.476
6.893
89
670.7 16
7.249
677.964
7.309
685.274
7.370
692.644
7.431
7.493
90
745.968
7.870
753.838
7.934
761.771
7.998
769.769
8.062
700.075 777.832
91
827.584
836.109
a.660
853.361
8.728
862.089
8.797
915.911
925.126
8.592 9.286
844.701
92
8.525 9.215
9.358
943.770
9.430
953.200
93
011.303
021.245
10.016
051.520
124.828
10.783
1 135.611
1041.353 1 146.473
10.167
114.124
10.091 10.862
9.502 10.243
94
9.942 10.705
934,4 12 11031.261
10.941
157.414
11.020
95
224.740
236.244
11.587
1 247.831
11.669
1259.500
11.752
271.252
11.835
96
343.525
11.505 12.342
355.868
12.428
12.515
1380.811
12.601
393.412
12.688
97
470.860
13.218
484.079
13.308
1.368.296 1 497.387
13.398
1510.785
13.489
524.274
13.580
98
607.129 752.724
14.133 15.088
621.263
14.227
14.321
1649.811
14.415
664.226
14.510
767.811
15.185
11535.490 1 782.996
1798.279
15.382
813.661
15.480
99 -
6.162
15.283
-
8.127
I,
THE
mm. Hg at 0°C and standard i-in “K __ 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 a0 a1 a2 a3 a4 a5 86 a7 aa a9 90 91 92 93 94 95 96 97 98 99 -
.5 1.1507 1.5653 2.1045 2.7981 3.6811 4.7947 6.1 a62 7.9099 10.0276 12.6090 15.7326 19.4854 23.9643 29.2756 35.5359 42.8722 51.4221 61.3341 72.7680 85.8942 100.8947
.0366 .0479 .0619 .0792 .I003 .1258 .1565 .1930 .236 1 .2a66 .3454 .4135 .49la .5al3 .6830 .79ao .9274 1.0722 1.2336 1.4126 1.6105 117.9624 1.a282 137.3015 2.0670 159.1273 2.3279 183.6656 2.6121 211.153 2.920 241.838 3.254 275.977 3.614 313.839 4.001 355.700 4.417 401.849 4.862 452.580 5.337 508.200 5.843 569.022 6.38 I 535.368 6.95 1 707.568 7.555 785.959 a.193 870.886 8.866 962.701 9.574 361.762 10.319 168.434 11.100 283.088 i 1.919 406.100 12.776 537.854 13.671 678.736 14.605 829.141 15.580
VAPOUR
PRESSURE
OF LIQUID
821
OXYGEN
gravity .6
1.1873 1.6132 2.1664 2.8772 3.7814 4.9205 6.3427 a. 1029 10.2636 12.8956 16.0780 19.8990 24.456 1 29.8569 36.2189 43.6702 52.3494 62.4063 74.0015 87.3068 102.5051 119.7906 139.3686 161.4552 186.2777 214.074 245.092 279.592 317.841 360.118 406.711 457.917 514.043 575.403 542.3 19 715.123 794.152 379.752 972.275 372.081 179.534 295.007 418.876 551.525 693.342 844.721
.0376 .0491 .0634 .oall .1026 .1286 .159a .1969 .24oa .2921 .35la .4209 .5003 .5909 .6939 .a103 .9411 1.0875 1.2506 1.4315 1.6313 1.8512 2.0921 2.3553 2.6418 2.953 3.289 3.652 4.042 4.460 4.908 5.386 5.895 6.436 7.010 7.617 a.259 a.935 9.647 10.395 i 1.180 12.003 12.863 13.763 14.701 15.679
5
.7
1.2249 1.6623 2.2298 2.9583 3.8840 5.0492 6.5025 a.2998 10.5044 13.la77 16.4298 20.3199 24.9564 30.4478 36.9128 44.4804 53.2906 63.4939 75.2522 88.7383 104.1365 121.6418 141.4607 163.8105 188.9195 217.027 248.381 283.243 321.882 364.578 411.619 463.303 519.938 581.839 649.329 722.740 802.41 i 888.687 98 1.922 082.476 190.714 307.009 431.739 565.287 708.043 860.400
.a .03a7 .0504 .0650 .0830 .1050 .1315 .I633 .2010 .2455 .2977 .3583 .4283 .5oaa .6006 .7049 .a227 .955 1 1.1031
1.2679 1.4506 1.6524 1.8743 2.1174 2.3829 2.6718 2.985 3.324 3.689 4.082 4.504 4.955 5.436 5.948 6.492 7.069 7.680 a.325 9.004 9.720 10.472 11.261 12.087 12.952 13.855 14.797 15.779
1.2636 1.7128 2.2949 3.0413 3.9890 5. i a07 6.6658 a.5008 10.7499 13.4854 16.7881 20.7482 25.4652 3 i .0485 37.6177 45.3031 54.2456 64.5970 76.5201 90.1 a90 105.7889 123.5161 143.5781 166.1934 191.5912 220.012 251.705 286.933 325.965 369.082 416.573 468.739 525.886 588.331 656.398 730.420 810.735 897.691 991.642 092.948 201.975 319.096 444.691 579.142 722.840 876.179
.9 .0397 .0517 .0667 .0851 .1074 .1344 .1668 .2051 .2504 .3033 .3649 .4359 .5175 .6105 .7161 .a353 ,969 1 1.1188 1.2854 1.4699 1.6737 1.8976 2.1429 2.4107 2.7020 3.018 3.359 3.727 4.123 4.547 5.001 5.485 6.001 6.548 7.129 7.743 a.391 9.074 9.794 10.549 11.342 12.172 13.040 13.947 14.893 15.880
1.3033 .0408 1.7645 .053 1 2.3615 .0684 3.1264 .oa71 4.0964 .1099 5.3151 .1374 6.8326 .1703 8.7060 .2094 11.0003 .2553 13.7887 .309 1 17.1530 .3715 21.1841 .4436 25.9826 .5262 31.6590 .6205 38.3338 .7274 46.1384 .a480 55.2147 .9834 65.7158 1.1347 77.8054 i .3030 91.6589 1.4894 107.4625 1.6951 125.4137 1.9212 145.7210 2.1687 168.6041 2.4387 194.2932 2.7324 223.030 3.05 1 255.065 3.395 290.660 3.766 330.088 4.164 373.629 4.59 1 421.575 5.048 474.224 5.536 531.887 6.054 594.880 6.605 663.527 7.189 738.162 7.806 819.126 a.458 906.766 9.145 00 1.436 9.868 103.497 10.627 213.317 11.423 331.268 12.257 457.731 13.129 593.089 14.040 737.733 14.990 892.058 15.980
822
THE
VAPOUR
PRESSURE
The change of the coefficients
OF LIQUID
OXYGEN
of eq. (3) to obtain eq. (4) changes dp/dT
at the boiling point only O.O56o/o. The value of dp/dT still agrees within experimental for it using Clapeyron’s
at the boiling point
error with the value that can be calculated
equation
and the available
experimental
data for
L, VG and VI,. Eq. (4) is a very good representation of our experimental data and is consistent with the available information thermodynamic
relation.
P-T
It describes
used in the calculation
of the
the pressure of the saturated
vapour of liquid oxygen as a smooth function of TBI and enables to obtain temperatures on the BI scale between 96 and 54.35”K from accurately measured vapour pressures with high precision and without the use of platinum thermometers. The BI scale is today’s most accurate realization of the thermodynamic temperature scale between 96 and 20°K. Without vapour pressure measurements the BI scale can be realized only to the highest precision using platinum thermometers compared directly or indirectly with a primary standard platinum thermometer at NBS, NPL, PRMI
or PSU.
Acknowledgements. We wish to thank Dr. M. Durieux for helpful discussions and reading of the manuscript and Mr. H. Kossen and Mr. E. H. V o ssep oel for their help with the measurements and the calculations. Received
lo-IO-65
REFERENCES 1) Van 2)
Dij k, H., Commun.
Mullins,
J.
Engineering 3)
Experiment
Hirschfelder, (J. Wiley
4)
Woolley,
5)
Barber,
7) 8)
Station,
and Sons Inc.,
Georgia
Lab.,
New York,
N.Y.,
Leiden
Institute
Molecular
No. 1. M. R., Muijlwijk,
R. and Van
theory
Note TM 3272,
de Thermometric
Document
du Cornit
Consultatif
945.
No. A-593
Dijk,
de Thermometric
1956.
H., Commun.
International
of the Comite
et Mesures
1964
Leiden
(1966) 900. Durieux, M., Muijlwij k, R. and Van Dij k, H., Meeting of the Cornit m6trie at the Bureau International des Poids et Mesures 1964 (Sevres, 42, Sessions
(1966)
of gases and liquids
at the Bureau
No. 0. D. I., Meeting
Astrov, D. N., Orlova, M. P. and Charevskaya, de Thermometric at the Bureau International des Poids Document Moussa,
32
No. 2, Project
1954, p. 163 f.f.).
Consultatif
1964 (S&vi-es, France)
Physica
report
of Technology. R. B.,
W. S., NACA Techn.
of the Cornit
No. 346a;
B. S., Technical
C. F. and Bird,
H. W. and Benedict, C. R., Meeting
Onnes
W. T. and Kirk,
J. O., Curtiss,
des Poids et Mesures 6)
Kamerlingh
C., Ziegler,
Consultatif
(Sevres,
No. 3466;
France),
Physica
32
Consultatif de ThermoFrance), Document No.
1964, to be published.
9) 10)
Hoge, H. J., J. Res. Nat. Bur. Stand., Washington 44 (1950) Orlova, M. P., Temperature, its measurement and control (Reinhold, New York, N.Y., 1962) Part 1, p. 179.
11)
Consultatif Orlova, M. P., Charevskaya, D. I. and Astrov, D. N., Meeting of the Cornit de Thermomgtrie at the Bureau International des Poids et Mesures 1964 (Sevres, France),
12)
Document No. 2.. Barber, C. R. and Horsford,
Miss
A., Metrologia,
321. in science
Vol. 1 (1965)
75.
and industry,
vol.
3
Physica
R.
Moussa,
Dijk,
32
805-822
M. 1~. H.
1966
THE VAPOUR
PRESSURE
by R. MUIJLWIJK, Communication
OF LIQUID
M. R. MOUSSA”)
No. 346~ from the Kamerlingh
OXYGEN
and H. VAN
Onnes Laboratorium,
DIJK
Leiden,
Nederland
Synopsis From
a thermodynamic
saturated
vapour
information. of the
apparatuses. from
compared
temperatures by a smooth The triple
pressure
thermometers
PRMI
KPL
the platinum
Fig. 5 shows
carried
were previously
and
oxygen out
p-T
thermometer
and
in two
calibrated
respectively.
that their difference
of the
experimental
of liquid
were
using the thermodynamic from
of the pressure
available
on the
Temperatures relation
were
readings.
The
can be represented
curve. point
at the triple point 54.350”K.
derived
using
of the vapour
thermometers
PSU,
measurements equal.
dependence
calculated
of platinum
of NBS,
temperatures
are nearly
was
measurements
The platinum
scales
the pressure
with
the temperature
oxygen
of a number
gas thermometer derived
equation
liquid
Simultaneous
resistance
different
of
of oxygen
was also measured.
We
1.0975 mm Hg at 0°C and standard
A formula
for the P-T
relation
of oxygen
found gravity
for the vapour
pressure
and for the temperature
is proposed
and a table has been
calculated.
The relation between the vapour pressure of liquid 1. Introduction. oxygen and temperature (p--T relation) can be obtained from measurements of p and T, and from thermodynamic calculations. The accuracy of the result obtained from measurements of p and T is mainly limited by the inaccuracies of the gas thermometric measurements.The use of a thermodynamic P-T relation helps us to avoid or to eliminate irregularities contained in the gas thermometric results. The accuracy of the thermodynamic P-T relation is limited by the accuracy of the data for thermodynamic quantities, which are used in the calculations. An accurate p-T relation was obtained by representing our results obtained from p and T measurements in an equation, that satisfies the requirements of thermodynamics within the limits of the available experimental data. The study of the p--T relation for liquid oxygen is of interest in several respects. a. This relation is used in thermometry to derive temperatures from measured vapour pressures. b. If the p-T relation is known accurately temperature scales, which are *) Mission member
of the National
Research
-
Centre of Egypt.
805
-
806
R. MUIJLWIJK,
based on the thermometers, a function calculations
of the
P-T
with the P-T
An accurate
H. VAN
knowledge
DIJK
calibrated the vapour
against gas pressure as
on such a scale.
of fi and T is an excellent
a.
AND
use of platinum thermometers can be checked by measuring
of temperature
A comparison
C.
M. R. MOUSSA
relation
relation
obtained
obtained
from
thermodynamic
from direct measurements
way to check the consistency
of both results.
of the vapour pressure-temperature
relation
of
liquid oxygen enables us to calibrate secundary thermometers (usually platinum thermometers) accurately between 54 and 100°K. In this paper a thermodynamic P-T relation for the saturated vapour of liquid oxygen and for temperatures between 54 and 100°K is given and discussed in section 2. A description of our apparatus is given in section 3. In section 4 the experiments and the method used to convert the experimental data in temperatures are described. In section 5 the experimental results are given. In section 6 our results are discussed and represented in a formula. 2. The thermodynamic p-T relation. a. Introduction. It can be shown from thermodynamicsi) that the vapour pressure-temperature relation for the saturated vapour of liquid oxygen can be written as: ln@/pi)
= A(1 -
In this equation The heat due T =
Tr/T) + ln(T/Ti)
+ 11 -
1s + 1s + 8 -
pi is the vapour pressure at a reference
~1.
temperature
(1) T1
constant A is equal to L(Tl)/RTl - 1 - 71, where L(Tl) is the molar of vaporization at T1 and R the gas constant. E and r] are corrections to the non-ideality of the gas, ~1 and 71 are the values of E and q for T1. II = ;(C,
-
C.,)/RT
dT
1’1 1s
=
(l/RT) /‘CC, -
Cvt) dT
Tl
I3 = (1 /RT) J%n(dp/dT)
dT;
T1
CL and Vn are respectively, the molar heat capacity and the molar volume of the liquid, C,, is the molar heat capacity of the gas at such a large molar volume, Vi, that the gas can be treated as an ideal gas. For liquid oxygen, C,, = #R. All terms in eq. (1) can be computed today with a reasonable precision for temperatures between 100°K and 54.35”K using available experimental information. The data needed to compute the vapour pressure b. Computations. of oxygen using eq. (1) have been gathered and discussed by Mullins,
THE VAPOIJR
I
+20
-10
t
T
1. Temperature according
.
I
I
70
equivalent
to different
of
I I
the
differences
OK
90
in
vapour
calculations.
TABLE
I (00
I
I
80
thermodynamic
807
OXYGEN
I
60
1
OF LIQUID
I
I
50
pig.
PRESSURE
pressure
Explanation
of
oxygen
in the text.
I
Abstract of the evaluation of the thermodynamicvapour pressure-temperature relation for liquid oxygen T
“K
Ziegler
and
Kirk
temperatures and pressure matical
they
result
Institute
They
calculated
100 and 54.352 T1 =
E -
P mm Hg at 09
El
1.344 5.459 17.554 47.073 109.354 226.437 427.149 746.584 1225.224 1908.022
- 0.03064 -0.03018 -0.02912 - 0.02707 -0.02359 -0.01822 -0.01059 -0,00039 +0.01258 - + 0.02846
90.168”K
“K.
the vapour
For
0.3080 + 0.2549 +0.2140 +0.1818 +0.1562 $0.1356 +0.1188 +0.1050 + 0.0935 + 0.0839 +
assistant
Using
at the Mathe-
essentially
the same representation
the same
of these data,
at 91 = 760 mm Hg at 0°C he got very nearly
differences An abstract
for
equal
fig. 1 where
pressures
of the main
at 25
temperature
at $1 = 760 mm Hg at 0°C. These
of Leiden.
This can be seen from
1 In P/dT “K-1
pressure
the reference
for us by Mr. W. Nuy,
of the University
90.170”K
temperature table
used
B liter mole-l -0.54949 -0.46496 - 0.40069 - 0.35031 - 0.30981 - 0.27660 - 0.24890 - 0.22545 -0.20536 - 0.18796
data and very nearly
as MZK.
and MZK.
-0.00602 - 0.00549 - 0.00499 - 0.00446 -0.00381 -0.00295 -0.00174 - 0.00007 + 0.00223 + 0.00529
were repeated
thermodynamic but T1 =
13
(MZK)2).
between
calculations
-
VL cm3 mole-’ +24.771 +25.156 + 25.562 + 25.993 + 26.450 + 26.938 +27.461 + 28.024 + 28.635 +29.300
I1 - 1%
results
curve
between
the same
A represents
the
results
of the calculations
the
of Nuy
is given
in
I.
To calculate Lennard-
Jones
e/k = 112°K
the second
virial
6-l 2 potential and
bo =
coefficient
function
for the vapour,
characterized
60.84 cm3 mole- 1. Different
MZK
used
a
by the two parameters values
for these
para-
808
R. MUIJLWIJK,
M. R. MOUSSA
meters were given by Hirschfeldera) Hirschfelder and Benedict
AND
H. VAN
DIJK
and by Woolley
-_____.
and BenedictJ).
gives e/k = 118 “K and bo = 52.25 cmsmole-1. give e/k = 116 “K and bo = 54.7 cmsmole-1.
MZK chose the parameters
in such a way that they obtained
Woolley agreement
with the $--T data of Hoge. Nuy
duplicated
and bo instead
his computation
of the MZK values.
using
Hirschfelder’s
data
for e/k
Curve B in fig. 1 shows the differences
between the first and the second computation of Nuy. The difference at 54 “K is about 16 m”K. To estimate the total uncertainty in the p-T relation calculated in this way, the uncertainties arising from possible errors in L(T), CL and Vn have to be added. The uncertainties due to uncertainties in CL and Vn are small and very small. The influence of the uncertainties can be reduced if we know the pressures (pi and Pz) of the saturated vapour; at two temperatures (T1 and Tz) sufficiently accurately. The constant A can then be eliminated from eq. (1) and the equation can be written: TZ T2 -
Ti
ln p-C(T2,TlJ}(1 PJ1
-l)iln$-
CCT,Td
P1T2
where C(T, TI) = Il(T, Tl) - Is(T, TI) + Is(T, T1) + E - cl. The coefficient of [l - (Tl/T)] in eq. (2) is slightly depending on the values chosen for e/k and bo, but equation (2) will always give pi at T1 and ps at Ts. When the results of Nuy’s first and second computation were made to agree at the boiling point and near the triple point of 0s by changing the coefficient A a little, the maximum difference in temperature for equal pressure reduced to only 6 m”K. The temperature dependence of this difference is shown in fig. 1 curve C. The changes in A that we need to reconcile the results of both computations and our experimental data for p and T at the triple point are smaller than 0.1 y0 and are well within the uncertainty of the experimental data available to calculate A. 3. Afiparahs. The vapour pressure-temperature relation for the saturated vapour of liquid oxygen was measured at many temperatures from 96 to 54.35”K. The temperature was measured with resistance thermometers which were calibrated on the NBS, PSU, PRMI or NPL gas thermometer scales below 90 “K. The vapour pressure was measured above 5 cm Hg with a mercury manometer and below 5 cm Hg with an oil manometer. Two different apparatuses were used. In the first apparatus, A (see fig. 2), four platinum thermometers were placed in holes in a copper block which was suspended in a metal can. Usually approximately 8 cm3 of liquid oxygen was condensed in this can so that the block was partly immersed. The inner can was separated from the surrounding oxygen bath by a jacket in which gas could be admitted. By changing the pressure of the gas the
THE
VAPOUR
1
PRESSURE
OF LIQUID
809
OXYGEN
1
86
80
k-40-q
r -7 C
I-z4
46
Fig. 2a.
Apparatus
A.
Fig.
2b.
Apparatus
B.
810 heat contact The jacket
K.
MUIJLWIJK,
between surrounded
M. Ii. MOUSSA
In this apparatus of Standards
DIJK
bath could be varied.
also the lower part of the capillary, to avoid condensation
there was a radiation
in the capillary.
were used:
No. 113760 1 (LN), calibrated
in Washington
which connected
shield.
the following thermometers
Leeds and Northrup
H. VAN
the inner can and the oxygen
the inner can with the manometers, Below the capillary
AND
on the NBS-1955
at the National Bureau
scale,
Tinsley No. 153371 (NPL 1) calibrated at the National Physical Laboratory in Teddington on the NPL scale, T 4, calibrated at the Physico-Technical and Radio-Technical Measurements Institute in Moscow on the PRMI scale, KOL 143, constructed in our laboratory and compared previously with LN No. 1137601. This apparatus was also used to measure the triple point pressure and temperature. The second apparatus, B (see fig. 2), consisted of a copper block in which 8 thermometers were inserted in holes around a central cavity. In this central cavity oxygen gas could be condensed through a capillary, connecting the cavity with the manometer system. The capillary was surrounded by a jacket, which was usually evacuated. There was a radiation shield inside the capillary just above the block. The copper block was surrounded by a not entirely closed copper shield fixed to the top of the block. This shield served to reduce vertical temperature gradients in the block, which are caused by the hydrostatic pressure differences in the bath. This apparatus was not suitable for triple point measurements, but the replacement of thermometers was much easier than in apparatus A. The thermometers used in this apparatus were: State University on PSU 1577534 (PSU 4), calibrated at the Pennsylvania the PSU scale calibrated at PRMI on the PRMI scale. T 4, NBS 1575702 (NBS 2), calibrated calibrated Tinsley 164956 (B 2)) PSU 1577533 (PSU 3), calibrated calibrated T 2, calibrated LN 1137601 (LN), NPL 153373 (NPL 3), calibrated
at at at at at at
NBS NPL PSU PRMI NBS NPL
on the NBS- 1955 scale on the NPL scale on the PSU scale on the PRMI scale on the NBS-1955 scale on the NPL scale.
The thermometers PSU 3, PSU 4, NBS 2, T 2 and NPL 3 were used previously for the international comparison of the 4 scales mentioned above at NPL5) and at PRMIS). The thermometers T 4 and LN were also used were made with these two in apparatus A, most of our measurements thermometers. The data for the thermometers KOL 143 and B 2 will not with be given here. In these two pieces of apparatus also measurements nitrogen 7), hydrogens) and helium were carried out.
THE
VAPOUR
PRESSURE
OF LIQUID
811
OXYGEN
The experiments consisted in simultaneous measurements 4. Ex$eriments. of the vapour pressure of oxygen and of the resistance of platinum thermometers. Temperatures were derived from the measured vapour pressures using a table calculated by N uy. This table gives the pressures and pressure differences in steps of O.l”K between 54 and 100°K. The data of the table are calculated with the equation: r”log fi = 28.888394 -
10.5434702 lolog T + 0.01934976 T + -
1880.776
666.13713 +
T
(3)
T2
where fi is expressed in mm Hg at 0°C and standard gravity and T in “K. This equation represents the 25 fi-T data of MZK for temperatures from
Fig. 3 50
1
50
T
60
70
80
70
5.0
90
OK
100
300
250
200
106,w I 150 ,60
90
OK
100
Fig. 4
Fig. 3 and 4. Differences in W = (R/2&,) between thermometers as obtained from our measurements compared with the averaged result from the measurements at NPL and at PRMI. 0 02 measurements q Nz measurements
812
MUIJLWIJK,
Ii.
Ill. K. MOUSSA
54.35 to 100°K with a standard
deviation
AND
H. VAN
DIJK
of only 0.14 m”K and a maximum
deviation of 0.27 m”K. To obtain temperatures according to Nuy’s first thermodynamic calculation mentioned in section 2 a graph was used. The graph between
shows the
the differences
result
of Nuy’s
and the calculation
in temperature
first
for equal
thermodynamic
with eq. (3). This graph
pressure
calculation
gives curve
with
values eq. (1)
A of fig. 1 on a large
scale. Temperatures
according
to Nuy’s
first thermodynamic
calculations
with
eq. (1) were denoted T,. From the reduced resistance W = K(T)/R (O’C), of the thermometers temperatures were derived on the RI scale. The BI scale is a smoothed average of four gas thermometer scales (NBS, PSU, NPL and PRMI scale). It is obtained from the rtlsult of the intercomparison of scales at NPL5) and PRMIa) and is described briefly in the appendix of our paper on the vapour pressure of nitrogen’). For the data near the boiling point and at the triple point, temperatures were derived also on the NBS, PSU, NPL and PRMI scale and on the reduced scales (see section 6 and the appendix mentioned above). The trmpcrature drift during the experiments was nearly always between 1 and 0.5 m “K per minute. The accuracy of the resistance measurements can be estimated from fig. 3 and 4. In these figures the differences in W between different thermometers are given together with a smooth average of these differences as reported by NPL and PRMI. The equivalent of 1 m “K is in the whole temperature range approximately 4 x 1OW in IV. 5. Experivaental results. a. Temperature 96 “K. The measured pressures and temperatures
50
Fig. 5. Differences thermometers
--
T
60
between
and expressed 0
80
70
temperatures
deduced
range between 54.35 and and the differences between
90
OK
from measurements
100
with platinum
on the HI scale and temperatures, T,, deduced pressure measurements. Apparatus I3 0 Apparatus .4
from vapour
THE
VAPOUR
PRESSURE
OF LIQUID
TABLE Differences thermometer -
between
the temperatures
measurements
pressure measurements.
II
on the BI scale deduced
and temperatures,
(The meaning
813
OXYGEN
T,,
of w is explained
Apparatus
from platinum
deduced
from
in section
vapour 6)
A
28. a.363
18.469
65.2386
136373
47.997
70.1071
157032
65.2462 70.1157
7.6
29. 8.‘63
8.6
29. a.‘63
225.34
79.9643
199539
79.9759
11.6
29. a.‘63
431.07
85.0768
221728
85.0881
11.3
29. 8.‘63
780.57
90.4262
244940
90.4328
6.6
2. 9.‘63
773.93
90.3446
244590
90.3522
7.6
2. 9.‘63
771.37
90.3123
244450
90.3199
7.6
54.3476
91959
54.3496
2.0
15.10.‘63
178.05
78.2696
192194
78.2807
11.1
15.10.‘63
345.08
83.2445
213774
83.2565
12.0
15.10.‘63
620.90
88.2801
235635
88.2899
9.8
130746
63.9046
6.5
24. 9.‘63
16.10.‘63
1.0975
13.804
63.898
85.495
I
73.460 1
171435
73.4734
29.
1.‘64
234.51
80.259 1
200820
80.2713
13.3 12.2
29.
1.‘64
296.46
82.0423
208552
82.0536
11.3
29.
1.‘64
476.76
85.9357
225453
85.9458
10.1
29.
1.‘64
599.71
87.9642
234258
87.9729
a.7
29.
1.‘64
748.57
243203
90.0327
7.3
30.
1.‘64
768.18
90.0254 90.2724
244283
90.2815
9.1
30.
1.‘64
664.92
88.91 IO
23837 1
88.9199
8.9
63.1051
127437
63.1118
6.7
2443 18
90.2895
a.6
16.10.‘63
24. 3.‘64
11.546
25. 3.‘64
768.86
90.2809
12. 5.‘64
70.5487
t 58929
70.5599
11.2
13. 5.‘64
51.97 771.14
90.3093
244442
90.3181
8.8
13. 5.‘64
771.52
90.3143
244458
90.3220
14. 5.‘64
344.79
83.2378
213733
83.247
14. 5.‘64
233.10
80.2140
200615
80.2240
10.0
14. 5.‘64
117.52
75.4638 62.1447
i 80045
75.4709
7.1
123440
62.1499
5.2
114355
59.9440
9.1
244425
6.1
Apparatus
B
26. 5.‘64
9.238
26. 5.‘64
59.9349
28. 5.‘64 28. 5’64
5.369 771.03 928.38
92.1287
252340
90.3142 92.1377
28. 5.‘64
1123.64
94.0841
260809
94.09’01
29. 5.‘64
1356.80
96.1043
269556
90.308
-
i
-
96.1083
7.7
i
9.3
9.0 6.0
-
4.0
values and the corresponding TBI values are given in table II and shown fig. 5. A smooth curve, showing no irregularities, yas drawn through the experimental points in fig. 5. This curve deviates nowhere more than 11 m”K from the zero line. The difference of 8 m “K at the boiling point is caused for 3 m”K by the differences between the BI scale and the average reduced scale (see fig. 6) and for 5 m”K by the fact that our realization of the boiling point temperature is 5 m”K different from the average result obtained at T,
in
814
K.
MUIJLWIJK,
SO&
M. R. MOUSSA
60
Fig. 6. Differences
70
between
AND
H. VAN
80
DIJK
OK
90
the BI scale and the average
reduced
100
scale.
the four other institutes. We will discuss this point in more detail in the sections 5b and 6. b. The boiling point. From the measurements near to the boiling point the resistance ratio R/R,,, was calculated at the boiling point. From these resistance ratio’s the temperatures T, were calculated. T, is the temperature on the scale on which each thermometer was calibrated (NPL, NBS-1955, PRMI or PSU scale). The results are given in table III. T,, denotes the temperature on each scale when it is reduced to the agreed values of the boiling points of oxygen and normal hydrogen (90.170”K and 20.384 “K respectively). TABLE Values obtained
for the boiling point of oxygen calibrated
r Thermometer
LN
1137601
III
at 4 different
Apparatus
A
with thermometers
institutes
I
Apparatus
B
Tn
‘Tnr
Tn
“K
“K
“K
OK
90.1857
90.1757
90.1813
90.1713
TW
NBS
1575702
90.1825
90.1725
PSU
1577533
90.1572
90.1762
PSU
1577534
90.1563
90.1753
NPL
153371
90.1046 90.2064
90.1746 90.1774
90.2075
90.1785
NPL
153373
PRMI
4
PRMI
2
90.1811
90.1711
90.2062
90.1772
The obtained reduced temperatures are 2-8 m”K higher than 90.170”K. The highest values were found for the PRMI thermometers. In the ideal case, that no errors were made in the determinations of the boiling point on each of the four scales and in the calibration of the thermometers on these scales, at each of the four institutes, and that there is no error in our measurements and no change in the calibration of the thermometers, T,, would be equal to 90.170”K. Our data for the boiling point of oxygen obtained from measurements near the boiling point with thermometers of the international group are compared in table IV with results obtained at NPL and PRMI. The 1963 data are deduced by means of interpolation from the comparison data communicated by Barber and Orlova to the members of the working
81:
THE VAPOUR PRESSURE OF LIQUID OXYGEN TABLE IV Comparison of thermometers 153372 243764.!
NPL 1963
of the international
-
-
NPL
90.179’ 90.169’
NPL NBS 153373 1575702 7 5 243767.8 243937.8 7 90.1803 90.1784”) 7 90.1703 90.1684 243758.7 243924.4 90.i 782 90.1753;) 7 90.1682 90.1653
243760.’ 7
PRMI 1963
group at the boiling point of oxygen
-
NBS
PRMI
PSU
T2
T3
1577533
1577: 24401
PSl
243697.5
;243706.2
244010.3
90.17918)
90.2007
90.2027
90.1523
90.1
90.1691
90.1717
90.1737
90.1713
90.1
243940.8
243957.7
243690.5
244002.1
24401
90. I 78’ ?
90.1770*)
90.1990
90.1504
90.1.
90.168’
90.1670
90.1700
90.1694
90.1
243757 243934 90.1778 90.1775*) 90.1681 3 90.1678 90.1675 90.1781 3
243786 243955 90.1846 90.1825*) 90.1746 90.1725
KOL 1964
90.1520
90.11
90.1702
90.1710
90.1’
244032
24403
90.2075
90.1572
90.11
90.1785
90.1762
90.1’
25.5359
25.5
25.5359
25.5
25.0894
-
24401
90.1992
243725
24.9830 25.5597 24.9831 25.5600 -
-
244009
24369 1
243757
PRMI 1964
PRMI
1575705
25.0895
-
*) NBS-1955scale **) RO before resp. after our measurements groups of the Comite Consultatif des Poids
et Mesures
by 0 rlova
de ThermomCtrie
(C.C.T.)
in 1963. The
to the same groups
at the Bureau Internationa
1964 data were communicated
in 1964. The
reduced
given in table IV differ always from 90.170 “K except they
are 90.170 by
90.170”K
temperatures
at the different
can be obtained
The boiling
main
institutes.
Average
values
at slightly
with
the PRMI
thermometer
of the results obtained
oxygen
with T2
with T4 and taken from the data mentioned This other thermometer
of PRMI
was calibrated
T2.
of the dT
only in two cases slightly The
data
differences
of table between
PRMI.
thermometer
the value 90.1773 obtained
in table III
is used in table V
in Moscow at the same time as in our laboratory.
values of table V from their average
values are
larger than 1 m”K.
V can be used to calculate the boiling
at the four other institutes. value
the value 90.1782 This
as in the liquid hydrogen
T2 and proved to be very stable during many measurements The deviations
frorr
different
for these difterence:
of table IV are used in table V except
at K.O.L. Instead
for the deviations
point was realized
gave too high values as well in the liquid region.
reason
Tnr
from the data given in table IV in the way shown in tabh
V. All data for T,, obtained
definition.
is, that the oxygen
temperatures,
in the few cases when
point temperatures
average realized
We can start this calculation
104 AT = 43 for KOL-NPL
as with the value
values
for the
at K.O.L.
and
as well with the
104 dT’=
61 for KOL-
The results are given in the columns a and b of table VI.
Column L
816
R. MUIJLWIJK,
M. R. MOUSSA
TABLE Average
values for the boiling point of oxygen
1
/
NPL
Measured NPL
/1.;:27 Tnr (AT 1 27 x
1041j .600[ Tnr
lo4 AT KOL-NPL KOL
at
PRMI
46
boiling
1 27
104 Al
1
PSU
-15 x 10411.;;15 ?‘nr
/IdT
-
1 12
the
4 Institutes
1
.i?
37
/ .1758 /
64
1
NBS
27 x 10411.k T”r
43
I.1746 I
between
points
46
I.17731
DIJK
V
I
jm
H. VAN
on the reduced scales and differences
realized pt’s from +
AND
1 33
49
-
43 _____
1.1725 1
.17505
57
61
KOL-PRMI PRMI 104m
I1;;.1701 I
19
I.16821
(
NPLPRMI
I27
/.1709/
PSU-
24
NPL
!l
I.16681
-18
.1690
’
NBSPSU
34
Differences boiling
TABLE Average
differences
points
VI
of the boiling
realized
of
realized
point
at different
temperatures
of oxygen
institutes
_-
(TKoL-TN).~@
I
h
1 L
37
46
/ (a + b +
(?‘KOL -
?‘NPL). 104
a 43
(7.~01, -
TPRMI). lo4
67
61
73
67
(TKOL -
TPSU)’
61
55
58
58
lo4
(TKOL. -
TNRS) IO4
(TKOL -
T,).
lo4
L)/3
42
27
21
25
24
495
435
505
48
gives the Leiden result, column (a + b + L)/3 gives the average of the columns a, b and L. The agreement of the results deduced from data obtained at different institutes is satisfactory. The boiling point realized at KOL is a little over 2 m”K higher than that realized at NBS, 4 m”K higher than that realized at NPL, about 6 m”K higher than that realized at PSU and about 7 m “K higher than that realized at PRMI. It is nearly 5 m”K higher than the average of the boiling points realized at the four other institutes. A lower boiling point will be realized when the oxygen contains some nitrogen. According to our experience oxygen obtained from potassium permanganate can be freed sufficiently from nitrogen by rectification. We prefer, however, to prepare our oxygen from the purest air free water by electrolysis and to free the oxygen from remainders of water and hydrogen by freezing and by fractionated distillation. c. The triple point. The triple point pressure and the triple point temperature were measured with apparatus A, by allowing the inner can to warm up slowly through the triple point. The pressure was measured with an oil manometer. The density of the Octoil-S used in the manometer was 0.9105 g cm-3 at 25°C. The cubic expansion coefficient was determined
THE
VAPOUR
between 19°C and 35°C
PRESSURE
OF LIQUID
817
OXYGEN
it was found to be 7.8 x 10-4°C-1.
Octoil-S and a high precision cathetometer
The use of the
enabled us to measure the vapour
pressure at the triple point with high accuracy. The result was ptr = 1.0975 mm Hg The temperature
at
0°C.
of the triple point was measured directly with the platinum
resistance thermometer LN 1137601. But because this thermometer was compared in the near vicinity of the triple point with the thermometers NPL 153371 and T4, the temperature of the triple point could be calculated from measurements on each of the 3 thermometers. The result is given in table VII. This result can be compared with results obtained by Hogeg) TABLE Temperature
of the triple point of oxygen
VII determined
with different
thermometers
(F., 1137601
54.3493
NPL
153371
54.3612
PRMI
T4
54.3616
LN
and by Orlovaie). Hoge’s triple point temperature on the NBS1939scale is 54.363”K, which corresponds to 54.353”K on the average reduced scale, reported the value 54.368”K. This corresponds to 54.356”K FIU. Orlova on the average reduced scale. Hoge’s result for the pressure of the saturated vapour at the triple point was fi = 1.14 mm Hg at 0°C. But since he also measured the values 1.12 and 1.13 mm Hg at 0°C the accuracy of his pressure measurements was apparantly not better than 0.02 mm Hg. 6. Disczlssion. and refiresentation of the results. four institutes NBS, PRMI, NPL and PSU thermometers
The individual scales of the are defined with standard
kept at the institute. Each institute compared
his (primary)
standard(s) with a gas thermometer at the institute and measured the temperature of boiling points of oxygen and hydrogen with its primary standard(s). The results obtained at the different institutes differ from each other as is shown in table VIII. These values differ for two reasons. TABLE The boiling
points of oxygen
and hydrogen
according CCT 1962 OK
VIII as recommended
to the different
NBS-1939 “K
individual NPL “K
by the CCT in 1962 and scales PRMI “K
PSU “K
02
90.170
90.190
90.180
90.199
90.151
n-Hz
20.384
20.3925
20.3875
20.394
20.365
818
R. MUIJLWIJK,
The main reason is, that different boiling
gas thermometric points
M. R. MOUSSA
different
H. VAN
DIJK
results have been obtained
measurements.
were not realized
AND
The second reason
at accurately
the
from the
is, that
the
same temperatures
in
the different atures,
institutes. To obtain a single generally acceptable scale temperon the individual scales were reduced with the aid of linear Tn,
reduction formulae to temperatures, T nr, on the reduced scales in such a way, that the declaredvalue for the normal oxygen boiling point becomes90.1700”K on its own reduced scale and the normal boiling point of normal hydrogen becomes 20.384”K. The scales reduced in this way are closer to each other but are not identic, not even at the boiling points. The differences between the individual reduced scales were measured at many temperatures by comparing thermometers calibrated at the four institutes. The results were confirmed by measurements at our institute. The comparisons enable to reduce the different scales to each other and also to their average, the average reduced scale (T,,), or to a proper continuous representation of it, as calculated by Orlova and othersii), the BI scale. The different values for Tnr at the boiling point of oxygen are shown in table V. We may conclude from this table, that, although T,, at the boiling point is 90.1700 on the individual reduced scales of the institutes NPL and PRMI, and is taken also 90.1700 for the boiling point realized at KOL, nevertheless the T,, values obtained from measurements on thermometers calibrated at other institutes differ from 90.1700”K. We may also conclude, that Tnr is 90. 17075 for the boiling point realized at NPL, is 90.1690 for the boiling point realized at PRMI and is 90.17505”K for the boiling point realized at KOL. Temperatures on the BI scale are at the boiling point of oxygen 2.7 m”K higher than temperatures on the average reduced scale (see fig. 6). The temperature of the normal boiling point of oxygen is therefore according to our recent measurements 90.1777 “K on the BI scale. This result is in close agreement with Barber’s result (90.182”K) obtained recently with the gas thermometer at NPLrs). Since the BI table is between 90.2 and 20°K a very good, well smoothed and well defined representation of the temperature dependence of a proper average*) of the reduced resistances of the platinum thermometers of the international group, and it was recommended for provisional use by the CCT in 1964, we compared our temperatures obtained from vapour pressure measurements with temperatures on the BI scale. According to table II deduced from vapour pressure measurements and fig. 5 temperatures T,, using Nuy’s first thermodynamic calculation and temperatures TBI, deduced from resistance measurements and expressed in the BI scale differ at the *) w = c4 FvPRMI2 + 2 WNPL’Z + 2 wNPL3 T,, = pn + 0.001952 - 0.0001325 T with
t- 2 WNBS2
+ WpSu3
+ FvpsuI)
j12;
Tn = (2 TPRMIZ + TNPL 2 + TNPL 3 + 2 TNBS~ + TPSU~ + TPSU 4) Ia, where for TNBS the NBS-1939 scale is used and NPL 2 refers to the NPL thermometer 153372.
819
THE VAPOUR PRESSURE OF LIQUID OXYGEN
boiling point nearly 8 m”K and at the triple point 2 m”K. A maximum difference of about 11 to 12 m”K was found at about 80 “K. These differences can be reduced considerably by using in the thermodynamic calculations the same value for the boiling point of oxygen as was obtained for it on the BI scale (90.1777”K). Still better agreement can be obtained by using for the calculation formula (2) and substituting for fis the accurately measured value for the vapour pressure at the triple point of oxygen (1.097jmm Hg at 0%) and for Ts the temperature of the triple point expressed on the BI scale (54.3496”K). Doing so the deviations at both fixed points become zero and the maximum deviation between both reduces to about 7 m”K. This maximum deviation is about the same as the remaining total inaccuracy in the thermodynamic calculations of the P-T relation. The deviation can be nearly reduced to zero by changing the constants used in the calculation of the virial corrections within the limits of the accuracy of the available data. In fact we used a slightly different method. Starting with eq. (3) we changed the coefficients of this equation a little in such a way, that at the boiling point and at the triple point temperatures the correct values for the vapour pressure were obtained and the average deviation for all measured temperatures became smaller than 0.2 m”K. We obtained the equation 10.534702 lolog T + 0.01932948 T +
r”log fi = 28.901847 -
667.85576
-
1937.538
T
$-
T2
(41
where fi is expressed in mm Hg at 0°C and standard gravity and T in “K. Fig. 7 shows the temperature equivalent of differences between our measured vapour pressures and vapour pressures calculated with eq. (4) from our measured temperatures expressed on the BI temperature scale. +5
o
m°K
0 0 0
0
0
000 I7
g-,““, “LO
+I
O
O
b
? tii c I -5 50
T
-60
70
80
90
OK
100
Fig. 7. Differences between temperatures on the BI scale and temperatures obtained using the revised P-T relation deduced from our measurements on platinum thermometers
and from
vapour
pressure
measurements.
Table IX gives the vapour pressure of liquid oxygen in mm Hg (OOC, standard gravity) according to eq. (4) at every tenth of a degree from 54°K up to 100°K and the differences between successive steps.
820
R. MUIJLWIJK,
M. R. MOUSSA
AND
H. VAN
DIJK
TABLE Vapour
-
.O
“K
I
.l
pressure
.2
of liquid
oxygen
i
I
c.f. eq. (4)
.3
.4
1.0804
.0347
1.1151
.0356
1.4733
.0454
1.5187
.0466
.0573
1.9853
.0588
2.0442
.0603
.0736
2.6454
.0754
2.7208
.0773
3.3940
.0935
3.4875
.0957
3.5832
.0980
.1150
4.4338
.1176
4.5514
.1203
4.6717
.1230
5.5930
.1435
5.7365
.1467
5.8832
.1499
6.033 1
.1531
7.1768
.1776
7.3544
.1813
7.5357
.1851
7.7209
8.9153
.1739 .2136
9.1290
.2180
.2224
9.5693
.2269
9.7962
.1890 .2314
63
11.2556
.2603
.2654
.2706
12.0520
.2758
12.3279
.2812
64
14.0978
.3149
11.5160 14.4127
9.3469 11.7814
.3208
14.7336
.3269
15.0604
.3330
15.3934
.3392
65
17.5245
.3783
17.9028
.3a51
18.2879
.3921
18.6800
.3991
19.0792
.4063
66
21.6277
.4513
22.0790
.4592
22.5383
.4672
23.0055
.4753
23.4808
.4a35
67
26.5089
.5351
27.0440
.5441
27.5881
.5532
28.1413
.5625
28.7038
.5718
68
32.2794
.6306
32.9100
.6408
33.5508
.6512
34.2020
.6617
34.8636
.6723
69
39.0612
.7388
.7504
41.3124
.7739
42.0863
.7859
46.9864
.8608
.8738
40.5503 48.7210
.7621
70 71
39.8000 47.8472
.8870
49.6080
.9003
50.5083
.9138
56.1981
57.1959
1.0123
58.2082
.0270
59.2353
1.0419
60.2772
1.0570
72
66.8504
.9978 1.1507
68.0012
1.1669
69.1681
.1833
70.3514
1.1999
71.5513
1.2166
73
79.1084
1.3208
80.4292
1.3388
81.7680
.3570
83.1250
1.3753
84.5003
1.3939
74
93.1483
1.5091
97.7355
1.5693
99.3049
1.5898
1.7168
1.5290 1.7387
1.549 1
109.1576
94.6575 110.8744
96.1 a65
75
112.6131
1.7607
114.3738
1.7830
116.1569
1.8055
76 77
127.3349
1.9449 2.1947
129.2798
1.9689
131.2487
1.9931
133.2418
2.0175
135.2594
2.0422
150.0844
2.2209
152.3052
2.2473
154.5525
2.2739
156.8264
2.3008
2.4670
173.5098
2.4956
176.0054
2.5243
178.5297
2.5533
181.0830
2.5826
54 1.4291
.0442
.0559
1.9280
.0718
2.5718
3.3027
.0913
.1124
4.3188
5.4525
.1404
61
7.0029
62
55
1.344 1
.0419
56 57
1.8176 2.4299
58
.043 1
.0545
1.3861 1.8721
.0701
2.5000
3.2135
.0892
59
4.2063
60
78
147.8897 171.0428
79
197.026
2.763
199.789
2.794
202.583
2.825
205.408
2.857
208.265
2.888
80
226.080
3.084
229.164
3.118
232.282
3.151
235.433
3.185
238.619
3.220
a1
258.459 294.426
3.431
261.890
3.467
265.357
3.503
268.861
3.540
272.401
3.577
3.804
298.230
3.843
302.073
3.882
305.956
3.922
309.878
3.96 1
82 83 84
334.252
4.206
338.458
4.247
342.705
4.289
346.995
4.332
351.326
4.374
378.220
4.636
382.856
387.537
4.725
392.262
4.771
397.033
85
426.623
5.096
431.718
4.680 5.143
436.862
5.191
442.053
5.239
447.292
4.816 5.288
86
479.760
5.586
496.670
5.739
502.410
6.108
490.983 550.2 11
5.688
537.941
485.346 544.049
5.637
87
556.426
6.270
562.697
5.791 6.325
88
601.484
6.662
608.146
6.719
/614.865
6.216 6.776
621.641
6.834
628.476
6.893
89
670.7 16
7.249
677.964
7.309
685.274
7.370
692.644
7.431
7.493
90
745.968
7.870
753.838
7.934
761.771
7.998
769.769
8.062
700.075 777.832
91
827.584
836.109
a.660
853.361
8.728
862.089
8.797
915.911
925.126
8.592 9.286
844.701
92
8.525 9.215
9.358
943.770
9.430
953.200
93
011.303
021.245
10.016
051.520
124.828
10.783
1 135.611
1041.353 1 146.473
10.167
114.124
10.091 10.862
9.502 10.243
94
9.942 10.705
934,4 12 11031.261
10.941
157.414
11.020
95
224.740
236.244
11.587
1 247.831
11.669
1259.500
11.752
271.252
11.835
96
343.525
11.505 12.342
355.868
12.428
12.515
1380.811
12.601
393.412
12.688
97
470.860
13.218
484.079
13.308
1.368.296 1 497.387
13.398
1510.785
13.489
524.274
13.580
98
607.129 752.724
14.133 15.088
621.263
14.227
14.321
1649.811
14.415
664.226
14.510
767.811
15.185
11535.490 1 782.996
1798.279
15.382
813.661
15.480
99 -
6.162
15.283
-
8.127
I,
THE
mm. Hg at 0°C and standard i-in “K __ 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 a0 a1 a2 a3 a4 a5 86 a7 aa a9 90 91 92 93 94 95 96 97 98 99 -
.5 1.1507 1.5653 2.1045 2.7981 3.6811 4.7947 6.1 a62 7.9099 10.0276 12.6090 15.7326 19.4854 23.9643 29.2756 35.5359 42.8722 51.4221 61.3341 72.7680 85.8942 100.8947
.0366 .0479 .0619 .0792 .I003 .1258 .1565 .1930 .236 1 .2a66 .3454 .4135 .49la .5al3 .6830 .79ao .9274 1.0722 1.2336 1.4126 1.6105 117.9624 1.a282 137.3015 2.0670 159.1273 2.3279 183.6656 2.6121 211.153 2.920 241.838 3.254 275.977 3.614 313.839 4.001 355.700 4.417 401.849 4.862 452.580 5.337 508.200 5.843 569.022 6.38 I 535.368 6.95 1 707.568 7.555 785.959 a.193 870.886 8.866 962.701 9.574 361.762 10.319 168.434 11.100 283.088 i 1.919 406.100 12.776 537.854 13.671 678.736 14.605 829.141 15.580
VAPOUR
PRESSURE
OF LIQUID
821
OXYGEN
gravity .6
1.1873 1.6132 2.1664 2.8772 3.7814 4.9205 6.3427 a. 1029 10.2636 12.8956 16.0780 19.8990 24.456 1 29.8569 36.2189 43.6702 52.3494 62.4063 74.0015 87.3068 102.5051 119.7906 139.3686 161.4552 186.2777 214.074 245.092 279.592 317.841 360.118 406.711 457.917 514.043 575.403 542.3 19 715.123 794.152 379.752 972.275 372.081 179.534 295.007 418.876 551.525 693.342 844.721
.0376 .0491 .0634 .oall .1026 .1286 .159a .1969 .24oa .2921 .35la .4209 .5003 .5909 .6939 .a103 .9411 1.0875 1.2506 1.4315 1.6313 1.8512 2.0921 2.3553 2.6418 2.953 3.289 3.652 4.042 4.460 4.908 5.386 5.895 6.436 7.010 7.617 a.259 a.935 9.647 10.395 i 1.180 12.003 12.863 13.763 14.701 15.679
5
.7
1.2249 1.6623 2.2298 2.9583 3.8840 5.0492 6.5025 a.2998 10.5044 13.la77 16.4298 20.3199 24.9564 30.4478 36.9128 44.4804 53.2906 63.4939 75.2522 88.7383 104.1365 121.6418 141.4607 163.8105 188.9195 217.027 248.381 283.243 321.882 364.578 411.619 463.303 519.938 581.839 649.329 722.740 802.41 i 888.687 98 1.922 082.476 190.714 307.009 431.739 565.287 708.043 860.400
.a .03a7 .0504 .0650 .0830 .1050 .1315 .I633 .2010 .2455 .2977 .3583 .4283 .5oaa .6006 .7049 .a227 .955 1 1.1031
1.2679 1.4506 1.6524 1.8743 2.1174 2.3829 2.6718 2.985 3.324 3.689 4.082 4.504 4.955 5.436 5.948 6.492 7.069 7.680 a.325 9.004 9.720 10.472 11.261 12.087 12.952 13.855 14.797 15.779
1.2636 1.7128 2.2949 3.0413 3.9890 5. i a07 6.6658 a.5008 10.7499 13.4854 16.7881 20.7482 25.4652 3 i .0485 37.6177 45.3031 54.2456 64.5970 76.5201 90.1 a90 105.7889 123.5161 143.5781 166.1934 191.5912 220.012 251.705 286.933 325.965 369.082 416.573 468.739 525.886 588.331 656.398 730.420 810.735 897.691 991.642 092.948 201.975 319.096 444.691 579.142 722.840 876.179
.9 .0397 .0517 .0667 .0851 .1074 .1344 .1668 .2051 .2504 .3033 .3649 .4359 .5175 .6105 .7161 .a353 ,969 1 1.1188 1.2854 1.4699 1.6737 1.8976 2.1429 2.4107 2.7020 3.018 3.359 3.727 4.123 4.547 5.001 5.485 6.001 6.548 7.129 7.743 a.391 9.074 9.794 10.549 11.342 12.172 13.040 13.947 14.893 15.880
1.3033 .0408 1.7645 .053 1 2.3615 .0684 3.1264 .oa71 4.0964 .1099 5.3151 .1374 6.8326 .1703 8.7060 .2094 11.0003 .2553 13.7887 .309 1 17.1530 .3715 21.1841 .4436 25.9826 .5262 31.6590 .6205 38.3338 .7274 46.1384 .a480 55.2147 .9834 65.7158 1.1347 77.8054 i .3030 91.6589 1.4894 107.4625 1.6951 125.4137 1.9212 145.7210 2.1687 168.6041 2.4387 194.2932 2.7324 223.030 3.05 1 255.065 3.395 290.660 3.766 330.088 4.164 373.629 4.59 1 421.575 5.048 474.224 5.536 531.887 6.054 594.880 6.605 663.527 7.189 738.162 7.806 819.126 a.458 906.766 9.145 00 1.436 9.868 103.497 10.627 213.317 11.423 331.268 12.257 457.731 13.129 593.089 14.040 737.733 14.990 892.058 15.980
822
THE
VAPOUR
PRESSURE
The change of the coefficients
OF LIQUID
OXYGEN
of eq. (3) to obtain eq. (4) changes dp/dT
at the boiling point only O.O56o/o. The value of dp/dT still agrees within experimental for it using Clapeyron’s
at the boiling point
error with the value that can be calculated
equation
and the available
experimental
data for
L, VG and VI,. Eq. (4) is a very good representation of our experimental data and is consistent with the available information thermodynamic
relation.
P-T
It describes
used in the calculation
of the
the pressure of the saturated
vapour of liquid oxygen as a smooth function of TBI and enables to obtain temperatures on the BI scale between 96 and 54.35”K from accurately measured vapour pressures with high precision and without the use of platinum thermometers. The BI scale is today’s most accurate realization of the thermodynamic temperature scale between 96 and 20°K. Without vapour pressure measurements the BI scale can be realized only to the highest precision using platinum thermometers compared directly or indirectly with a primary standard platinum thermometer at NBS, NPL, PRMI
or PSU.
Acknowledgements. We wish to thank Dr. M. Durieux for helpful discussions and reading of the manuscript and Mr. H. Kossen and Mr. E. H. V o ssep oel for their help with the measurements and the calculations. Received
lo-IO-65
REFERENCES 1) Van 2)
Dij k, H., Commun.
Mullins,
J.
Engineering 3)
Experiment
Hirschfelder, (J. Wiley
4)
Woolley,
5)
Barber,
7) 8)
Station,
and Sons Inc.,
Georgia
Lab.,
New York,
N.Y.,
Leiden
Institute
Molecular
No. 1. M. R., Muijlwijk,
R. and Van
theory
Note TM 3272,
de Thermometric
Document
du Cornit
Consultatif
945.
No. A-593
Dijk,
de Thermometric
1956.
H., Commun.
International
of the Comite
et Mesures
1964
Leiden
(1966) 900. Durieux, M., Muijlwij k, R. and Van Dij k, H., Meeting of the Cornit m6trie at the Bureau International des Poids et Mesures 1964 (Sevres, 42, Sessions
(1966)
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