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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		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	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

1	A. T. Van Urk, W. H. Keesom, and K. H. Onnes, "Measurements of the Surface Tension of Liquid Helium," Proc. Roy. Acad. Amsterdam 28, 958-962 (1925).
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3	B. N. Esel'son and Berezniak, “Surface Tension of 3He-4He Mixtures,” Dokl. Akad. Nauk. USSR 98, 569-571 (1954).
4	K. R. Atkins, “Third and Fourth Sound in Liquid Helium II,” Phys. Rev. 113, 962-965 (1959).
5	Y. Narahara, “The Surface Tension of Liquid 4He at Low Temperatures Near Lambda-Point,” Ph.D. Thesis, University of Pennsylvania, 1963 (unpublished).
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10	P. J. King and A. F. G. Wyatt, “Surface Waves on Liquid 4He,” Proc. Roy. Soc. Lond. A322, 355-359 (1971).
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