|
|
The
Observed Properties of Liquid Helium
at the Saturated Vapor
Pressure
Chapter
9. Surface Tension
Adopted
Database
Author(s) |
Key # |
Method |
Range (K) |
Iino
et al. |
1 |
Surface waves |
0.35
T
5.199 |
Magerlein
& Sanders |
2 |
Capillary rise |
-0.5 ,t,0.05 t = 1 - T / T |
Comments and Key to Authors
1)
Ref. 17. Data is absolute and revises the value of surface tension at
T=0 K to 354.4?0.5 mdyne/cm. Note that the temperature dependence of the
surface tension agrees with earlier data of Ekhart et al.16 almost exactly.
Uncertainty is ?0.3 mdyne/cm.
2) Refs. 13 & 15. We have incorporated this data set by adjusting
the absolute surface tension to fit the only two points overlapping Iino
et al. Uncertainty is ?0.03%.
3) On the original database, Tc was taken to be 5.199 K on the T58
scale. It has been corrected to 5.189 K. Upon conversion to ITS-90, Tc
= 5.1958 K.
4) According to M.R. Moldover 18 around (on the T58
scale), the surface tension can be expressed as
Table 9.1. Adopted database
for the surface tension of liquid 4He.
T90 (K) |
(N/m) |
Key |
T90 |
(N/m) |
Key |
0.000000 |
3.54400E-4 |
1 |
2.154326 |
2.88358E-4 |
2 |
0.100365 |
3.54370E-4
|
1
|
2.156094
|
2.88180E-4 |
2 |
0.200706 |
3.54240E-4
|
1 |
2.157890 |
2.88001E-4 |
2 |
0.301026 |
3.53990E-4
|
1 |
2.159730 |
2.87817E-4 |
2 |
0.401326 |
3.53600E-4 |
1 |
2.161561 |
2.87633E-4
|
2 |
0.501608 |
3.53040E-4 |
1 |
2.163420 |
2.87444E-4
|
2 |
0.601874
|
3.52300E-4
|
1
|
2.165243 |
2.87263E-4 |
2 |
0.702125
|
3.51360E-4 |
1 |
2.166176
|
2.87163E-4 |
2 |
0.802362
|
3.50200E-4
|
1 |
2.167094 |
2.87073E-4
|
2 |
0.902586
|
3.48770E-4
|
1 |
2.167131 |
2.87069E-4 |
2 |
1.002777 |
3.47040E-4
|
1
|
2.168069
|
2.86977E-4
|
2 |
1.102955 |
3.44970E-4 |
1 |
2.168971
|
2.86887E-4 |
2 |
1.203267 |
3.42510E-4 |
1
|
2.169895
|
2.86792E-4
|
2 |
1.303324 |
3.39590E-4
|
1 |
2.170832
|
2.86696E-4 |
2 |
1.403515 |
3.36170E-4 |
1 |
2.171979 |
2.86596E-4 |
2 |
1.503598
|
3.32160E-4 |
1 |
2.172908
|
2.86504E-4 |
2 |
1.603690
|
3.27510E-4
|
1
|
2.173388 |
2.86456E-4 |
2 |
1.703882 |
3.22160E-4 |
1 |
2.173840 |
2.86415E-4 |
2 |
1.804065 |
3.16060E-4
|
1
|
2.174321
|
2.86367E-4 |
2 |
1.904151 |
3.09160E-4 |
1
|
2.174679 |
2.86334E-4
|
2 |
2.004234 |
3.01470E-4 |
1 |
2.175047
|
2.86300E-4
|
2 |
2.079869 |
2.95624E-4 |
2 |
2.175435 |
2.86276E-4 |
2 |
2.082083 |
2.95431E-4
|
2
|
2.175795
|
2.86240E-4 |
2 |
2.087213 |
2.94947E-4 |
2 |
2.176193
|
2.86210E-4 |
2 |
2.092275 |
2.94469E-4
|
2 |
2.176591 |
2.86179E-4 |
2 |
2.097406 |
2.93974E-4 |
2 |
2.177009 |
2.86141E-4 |
2 |
2.102724 |
2.93466E-4 |
2 |
2.177009 |
2.86137E-4 |
2 |
2.104399 |
2.92980E-4
|
1 |
2.177399 |
2.86107E-4 |
2 |
2.107993 |
2.92960E-4 |
2
|
2.177827
|
2.86072E-4 |
2 |
2.113455 |
2.92430E-4 |
2 |
2.178246 |
2.86040E-4 |
2 |
2.118900 |
2.91894E-4
|
2
|
2.178666
|
2.86005E-4
|
2 |
2.124429
|
2.91342E-4 |
2
|
2.179057
|
2.85973E-4 |
2 |
2.128622 |
2.90927E-4 |
2 |
2.179459 |
2.85945E-4 |
2 |
2.132810
|
2.90504E-4 |
2 |
2.180023 |
2.85896E-4
|
2 |
2.136982 |
2.90092E-4 |
2 |
2.180618
|
2.85849E-4
|
2 |
2.141155 |
2.89676E-4 |
2 |
2.180915 |
2.85832E-4 |
2 |
2.143769 |
2.89418E-4 |
2 |
2.181194
|
2.85804E-4 |
2 |
2.146368
|
2.89154E-4 |
2 |
2.181721 |
2.85747E-4 |
2 |
2.149038 |
2.88883E-4
|
2 |
2.182695 |
2.85674E-4 |
2 |
2.151739 |
2.88615E-4 |
2 |
2.183738 |
2.85594E-4 |
2 |
Table 9.1. (continued)
T90 (K) |
(N/m) |
Key |
T90 |
(N/m) |
Key |
2.185086
|
2.85487E-4
|
2 |
2.605385 |
2.53500E-4 |
1 |
2.186419 |
2.85383E-4 |
2 |
2.705694
|
2.44660E-4
|
1 |
2.187845 |
2.85275E-4 |
2 |
2.805957 |
2.35360E-4 |
1 |
2.189845 |
2.85119E-4 |
2 |
2.906140 |
2.25630E-4
|
1 |
2.191956 |
2.84954E-4
|
2 |
3.006300 |
2.15530E-4
|
1 |
2.194914 |
2.84729E-4 |
2 |
3.106442
|
2.05110E-4 |
1 |
2.197996 |
2.84485E-4 |
2 |
3.206578 |
1.94460E-4 |
1 |
2.201022
|
2.84251E-4
|
2
|
3.306723 |
1.83640E-4
|
1 |
2.204070
|
2.84013E-4
|
2 |
3.406851 |
1.72730E-4 |
1 |
2.204624
|
2.84500E-4
|
1 |
3.506953 |
1.61810E-4
|
1 |
2.207112
|
2.83784E-4 |
2 |
3.607030 |
1.50920E-4
|
1 |
2.212391 |
2.83375E-4 |
2
|
3.707067
|
1.40130E-4
|
1 |
2.217529 |
2.82980E-4 |
2
|
3.807062
|
1.29490E-4 |
1 |
2.222839
|
2.82571E-4
|
2
|
3.907038
|
1.19020E-4
|
1 |
2.228186 |
2.82154E-4
|
2
|
4.007034
|
1.08740E-4
|
1 |
2.233636 |
2.81737E-4 |
2 |
4.107060 |
9.86700E-5 |
1 |
2.239167 |
2.81309E-4 |
2 |
4.207083
|
8.88000E-5 |
1 |
2.246959 |
2.80707E-4 |
2
|
4.306979 |
7.91200E-5
|
1 |
2.247050 |
2.80704E-4 |
2
|
4.406982 |
6.96100E-5 |
1 |
2.254904 |
2.80095E-4
|
2
|
4.507062 |
6.02400E-5 |
1 |
2.263157 |
2.79440E-4 |
2 |
4.607173 |
5.09800E-5 |
1 |
2.271323 |
2.78802E-4 |
2 |
4.707276
|
4.18300E-5 |
1 |
2.279781 |
2.78143E-4 |
2 |
4.807336 |
3.27600E-5 |
1 |
2.287614 |
2.77514E-4
|
2
|
4.907327 |
2.38000E-5 |
1 |
2.287627 |
2.77516E-4 |
2 |
5.007230 |
1.50500E-5 |
1 |
2.304706 |
2.77290E-4 |
1 |
5.107032 |
6.75000E-6 |
1 |
2.404936 |
2.69780E-4 |
1
|
5.195767 |
0 |
|
2.505156
|
2.61870E-4
|
1 |
|
|
|
Figure 9.1. The recommended
values of the surface tension of liquid 4He as a function of temperature
at saturated vapor pressure.
Table
9.2. Knots and coefficients for the spline fit of the surface tension
of liquid
Knots |
Coefficients |
K(1)
= 0.000000 |
C(1)
= 3.543998E-4 |
K(2)
= 0.000000 |
C(2)
= 3.545090E-4 |
K(3)
= 0.000000 |
C(3)
= 3.524383E-4 |
K(4)
= 0.000000 |
C(4)
= 3.366694E-4 |
K(5)
= 6.482413E-4 |
C(5)
= 2.921292E-4 |
K(6)
= 2.004234 |
C(6)
= 2.860852E-4 |
K(7)
= 2.176800 |
C(7)
= 2.796835E-4 |
K(8)
= 2.176800 |
C(8) = 2.747804E-4 |
K(9)
= 2.178377 |
C(9)
= 2.346234E-4 |
K(10)
= 2.412388 |
C(10)
= 1.357632E-4 |
K(11)
= 2.412896 |
C(11)
= 5.361123E-5 |
K(12)
= 3.807062 |
C(12)
= 1.263761E-5 |
K(13)
= 4.868895 |
C(13)
= 3.795854E-6 |
K(14)
= 5.035567 |
C(14)
= 5.599775E-12 |
K(15)
= 5.195767 |
|
K(16)
= 5.195767 |
|
K(17)
= 5.195767 |
|
K(18)
= 5.195767 |
|
Figure
9.2. Detail of the surface tension about the lambda transition.
Table
9.3. Recommended values of the surface tension of liquid 4He.
T90 (K) |
(N/m) |
T90 |
(N/m) |
0.1000
|
3.544E-4
|
2.3000
|
2.770E-4 |
0.1500
|
3.543E-4
|
2.3500
|
2.735E-4 |
0.2000
|
3.543E-4
|
2.4000 |
2.699E-4 |
0.2500
|
3.541E-4
|
2.4500
|
2.662E-4 |
0.3000
|
3.540E-4
|
2.5000
|
2.623E-4 |
0.3500
|
3.538E-4
|
2.5500
|
2.582E-4 |
0.4000
|
3.536E-4 |
2.6000
|
2.540E-4 |
0.4500
|
3.533E-4
|
2.6500 |
2.497E-4 |
0.5000
|
3.530E-4
|
2.7000
|
2.452E-4 |
0.5500
|
3.527E-4 |
2.7500 |
2.406E-4 |
0.6000
|
3.523E-4
|
2.8000 |
2.359E-4 |
0.6500
|
3.519E-4
|
2.8500
|
2.311E-4 |
0.7000
|
3.514E-4 |
2.9000
|
2.262E-4 |
0.7500
|
3.508E-4
|
2.9500
|
2.212E-4 |
0.8000
|
3.502E-4 |
3.0000
|
2.161E-4 |
0.8500
|
3.496E-4
|
3.0500
|
2.110E-4 |
0.9000
|
3.488E-4
|
1
3.1000
|
2.058E-4 |
0.9500
|
3.480E-4 |
3.2000
|
1.952E-4 |
1.0000
|
3.471E-4
|
3.3000
|
1.844E-4 |
1.1000
|
3.451E-4 |
3.4000
|
1.735E-4 |
1.2000
|
3.426E-4
|
3.5000
|
1.626E-4 |
1.3000 |
3.397E-4 |
3.6000
|
1.517E-4 |
1.4000
|
3.362E-4
|
3.6500
|
1.463E-4 |
1.5000
|
3.322E-4
|
3.7000
|
1.409E-4 |
1.5500
|
3.300E-4
|
3.7500
|
1.355E-4 |
1.6000 |
3.276E-4 |
3.8000
|
1.302E-4 |
1.6500
|
3.251E-4
|
3.8500 |
1.249E-4 |
1.7000
|
3.224E-4
|
3.9000 |
1.197E-4 |
1.7500
|
3.195E-4
|
3.9500 |
1.146E-4 |
1.8000 |
3.164E-4 |
4.0000 |
1.095E-4 |
1.8500
|
3.131E-4
|
4.0500
|
1.044E-4 |
1.9000
|
3.096E-4
|
4.1000 |
9.942E-5 |
1.9500
|
3.060E-4
|
4.1500
|
9.445E-5 |
2.0000
|
3.021E-4
|
4.2000
|
8.954E-5 |
2.0500
|
2.980E-4
|
4.2500 |
8.466E-5 |
2.1000 |
2.936E-4 |
4.3000
|
7.983E-5 |
2.1500
|
2.889E-4
|
4.3500 |
7.503E-5 |
2.1760 |
2.862E-4 |
4.4000
|
7.028E-5 |
2.1761
|
2.862E-4
|
4.4500
|
6.556E-5 |
2.1762 |
2.862E-4 |
4.5000 |
6.087E-5 |
2.1763 |
2.862E-4 |
4.5500 |
5.622E-5 |
2.1764
|
2.862E-4 |
4.6000 |
5.160E-5 |
2.1765
|
2.862E-4
|
4.6500
|
4.701E-5 |
2.1766
|
2.862E-4 |
4.7000 |
4.245E-5 |
2.1767
|
2.862E-4
|
4.7500 |
3.792E-5 |
2.1768 |
2.861E-4 |
4.8000
|
3.341E-5 |
2.1769
|
2.861E-4
|
4.8500 |
2.893E-5 |
2.1770
|
2.861E-4 |
4.9000
|
2.447E-5 |
2.2000
|
2.843E-4 |
4.9500 |
2.005E-5 |
2.2500
|
2.805E-4
|
5.0000 |
1.570E-5 |
Figure 9.3. The fractional
deviation of the values of the adopted database from the recommended values
of the surface tension of liquid 4He expressed in percent.
Chronological Bibliography for Entropy
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2 |
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3 |
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4 |
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6 |
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|
|