Russell J. Donnelly
541-346-4226 (Tel)
541-346-5861 (Fax)
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The
Observed Properties of Liquid Helium
at the Saturated Vapor
Pressure
Chapter
4. Second Sound Velocity
Adopted Database
Author(s) |
Key # |
Method |
Range (K) |
Uncertainty (%) |
| Heiserman et al | 1 | Resonance | 1.187
 T
2.150 |
< 0.2 |
| Greywall & Ahlers | 2 | Resonance | 2.16
T
2.172 |
< 0.2 |
| Tam & Ahlers | 3 | Resonance | 0.15
T
2.16 |
< 0.2 |
| Peshkov | 4 | Resonance | 0.5
T
1.15 |
0.75 |
| Wang et al. | 5 | Resonance |
1.187
T 1.804 |
0.07 |
| Lipa & Marek | 6 | Resonance | 1.13
T
2.09 |
see comment 6 |
Comments and Key to Authors
1)
Ref. 23. Points at 2.05 K and 2.15 K omitted as inconsistent with later
measurements.
2) Ref. 19. Data above 2.145 K omitted in favor of data of Greywall and
Ahlers.
3) Ref. 26.
4) Ref. 8. Data used only below 1.15 K, higher temperature data is inconsistent
with later measurements.
5) Ref. 27.
6) Ref. 28. Consists of points normalized to measurements of Greywall
and Ahlers at t=1-T/T 
=10-3.
Authors note that for t < 3x10-6 tests of the calculation
of superfluid density from second sound begin to deviate from the best
fit function.
7) The velocities are listed in m/sec. Multiply by 100 to convert to cm/sec.
Table 4.1. Adopted database for second sound velocity in helium II.
T90 (K) |
u2 (m/s) |
Key |
T90 |
u2 (m/s) |
Key |
| 0.551743 | 1.05000E+2 | 4 | 1.652076 | 2.03647E+1 | 5 |
| 0.601874 | 8.30000E+1 | 4 | 1.653078 | 2.03648E+1 | 5 |
| 0.651991 | 6.20000E+1 | 4 | 1.653779 | 2.04000E+1 | 1 |
| 0.702125 | 4.65000E+1 | 4 | 1.653779 | 2.03450E+1 | 3 |
| 0.752245 | 3.60000E+1 | 4 | 1.654080 | 2.03647E+1 | 5 |
| 0.802362 | 2.90000E+1 | 4 | 1.655082 | 2.03645E+1 | 5 |
| 0.852476 | 2.44000E+1 | 4 | 1.656084 | 2.03644E+1 | 5 |
| 0.902586 | 2.16000E+1 | 4 | 1.657086 | 2.03642E+1 | 5 |
| 0.952694 | 1.98000E+1 | 4 | 1.703882 | 2.03600E+1 | 2 |
| 1.002777 | 1.89000E+1 | 4 | 1.703882 | 2.02950E+1 | 3 |
| 1.052861 | 1.85000E+1 | 4 | 1.706888 | 2.03300E+1 | 1 |
| 1.102955 | 1.83300E+1 | 4 | 1.708993 | 2.03030E+1 | 5 |
| 1.122986 | 1.83000E+1 | 4 | 1.753981 | 2.01350E+1 | 3 |
| 1.137607 | 1.83754E+1 | 5 | 1.756986 | 2.01600E+1 | 1 |
| 1.137607
|
1.83742E+1 | 5 | 1.758690 | 2.01364E+1 | 5 |
| 1.83742E+1 | 1.83739E+1 | 5 | 1.804065 | 1.98900E+1 | 2 |
| 1.153029 | 1.83300E+1 | 4 | 1.804065 | 1.98450E+1 | 3 |
| 1.167152 | 1.84292E+1 | 5 | 1.808071 | 1.98800E+1 | 1 |
| 1.190093 | 1.84500E+1 | 1 | 1.808271 | 1.98395E+1 | 5 |
| 1.215134 | 1.85636E+1 | 5 | 1.808371 | 1.98381E+1 | 5 |
| 1.246176 | 1.87500E+1 | 1 | 1.854119 | 1.94200E+1 | 1 |
| 1.251399 | 1.87366E+1 | 5 | 1.854119 | 1.94000E+1 | 3 |
| 1.301319 | 1.90600E+1 | 1 | 1.857822 | 1.93832E+1 | 5 |
| 1.337208 | 1.92012E+1 | 5 | 1.904151 | 1.88000E+1 | 1 |
| 1.337409 | 1.91954E+1 | 5 | 1.904151 | 1.87800E+1 | 2 |
| 1.354445 | 1.93000E+1 | 1 | 1.904151 | 1.87550E+1 | 3 |
| 1.374079 | 1.93980E+1 | 5 | 1.904151 | 1.87620E+1 | 3 |
| 1.405517 | 1.95900E+1 | 1 | 1.907353 | 1.87314E+1 | 5 |
| 1.418729 | 1.96354E+1 | 5 | 1.954189 | 1.78400E+1 | 1 |
| 1.418829 | 1.96393E+1 | 5 | 1.954189 | 1.78640E+1 | 3 |
| 1.454558 | 1.98500E+1 | 1 | 1.954189 | 1.78700E+1 | 3 |
| 1.468770 | 1.98797E+1 | 5 | 1.957192 | 1.78245E+1 | 5 |
| 1.504599 | 2.01000E+1 | 1 | 1.976908 | 1.73749E+1 | 5 |
| 1.517108 | 2.00828E+1 | 5 | 2.004234 | 1.66800E+1 | 1 |
| 1.553637 | 2.02600E+1 | 1 | 2.004234 | 1.66380E+1 | 3 |
| 1.556640 | 2.02000E+1 | 3 | 2.006736 | 1.65832E+1 | 5 |
| 1.563245 | 2.02338E+1 | 5 | 2.026757 | 1.59588E+1 | 5 |
| 1.603690 | 2.03600E+1 | 1 | 2.036769 | 1.56137E+1 | 5 |
| 1.603690 | 2.03800E+1 | 2 | 2.046682 | 1.52424E+1 | 5 |
| 1.603690 | 2.03100E+1 | 3 | 2.054293 | 1.49260E+1 | 3 |
| 1.611903 | 2.03336E+1 | 5 | 2.054293 | 1.49350E+1 | 3 |
| 1.612103 | 2.03339E+1 | 5 | 2.056697 | 1.48429E+1 | 5 |
| 1.646264 | 2.03643E+1 | 5 | 2.066614 | 1.44125E+1 | 5 |
| 1.647266 | 2.03645E+1 | 5 | 2.076632 | 1.39451E+1 | 5 |
| 1.648168 | 2.03646E+1 | 5 | 2.084349 | 1.35550E+1 | 3 |
| 1.649170 | 2.03647E+1 | 5 | 2.086133 | 1.34778E+1 | 2 |
| 1.650172 | 2.03647E+1 | 5 | 2.086553 | 1.34370E+1 | 5 |
Table 4.1. (Continued)
T90 (K) |
u2 (m/s) |
Key |
T90 |
u2 (m/s) |
Key |
| 1.651174 | 2.03647E+1 | 5 | 2.096678 | 1.28791E+1 | 5 |
| 2.096777 | 1.28865E+1 | 2 | 2.169878 | 4.95010E+0 | 2 |
| 2.104399 | 1.24120E+1 | 3 | 2.170387 | 4.79702E+0 | 6 |
| 2.104399 | 1.24070E+1 | 3 | 2.170722 | 4.69640E+0 | 2 |
| 2.106209 | 1.23112E+1 | 2 | 2.171109 | 4.57153E+0 | 6 |
| 2.114429 | 1.17390E+1 | 3 | 2.171274 | 4.51860E+0 | 2 |
| 2.114572 | 1.17519E+1 | 2 | 2.171601 | 4.40753E+0 | 6 |
| 2.121978 | 1.12045E+1 | 2 | 2.172127 | 4.28890E+0 | 2 |
| 2.124462 | 1.09980E+1 | 3 | 2.172516 | 4.14923E+0 | 6 |
| 2.128512 | 1.06792E+1 | 2 | 2.172678 | 4.08362E+0 | 6 |
| 2.134262 | 1.01738E+1 | 2 | 2.172714 | 4.06910E+0 | 2 |
| 2.134497 | 1.01330E+1 | 3 | 2.173031 | 3.94628E+0 | 6 |
| 2.143812 | 9.21890E+0 | 2 | 2.173227 | 3.86140E+0 | 2 |
| 2.144531 | 9.15200E+0 | 3 | 2.173323 | 3.81918E+0 | 6 |
| 2.147768 | 8.77150E+0 | 2 | 2.173667 | 3.66760E+0 | 2 |
| 2.149547 | 8.53300E+0 | 3 | 2.173702 | 3.65415E+0 | 6 |
| 2.151231 | 8.34400E+0 | 2 | 2.174015 | 3.50552E+0 | 6 |
| 2.154307 | 7.93250E+0 | 2 | 2.174071 | 3.47580E+0 | 2 |
| 2.154563 | 7.87300E+0 | 3 | 2.174404 | 3.30200E+0 | 2 |
| 2.154563 | 7.88500E+0 | 3 | 2.174434 | 3.29027E+0 | 6 |
| 2.157027 | 7.53700E+0 | 2 | 2.174695 | 3.14020E+0 | 2 |
| 2.158715 | 7.24200E+0 | 3 | 2.174712 | 3.13242E+0 | 6 |
| 2.159393 | 7.16540E+0 | 2 | 2.174894 | 3.02889E+0 | 6 |
| 2.160303 | 7.02130E+0 | 6 | 2.174954 | 2.98440E+0 | 2 |
| 2.160601 | 6.92000E+0 | 3 | 2.175059 | 2.92025E+0 | 6 |
| 2.160728 | 6.94955E+0 | 6 | 2.175174 | 2.84060E+0 | 2 |
| 2.161555 | 6.80603E+0 | 6 | 2.175303 | 2.75214E+0 | 6 |
| 2.161688 | 6.77390E+0 | 2 | 2.175395 | 2.68280E+0 | 2 |
| 2.162195 | 6.63700E+0 | 3 | 2.175417 | 2.67168E+0 | 6 |
| 2.162543 | 6.62154E+0 | 6 | 2.175579 | 2.54290E+0 | 2 |
| 2.162797 | 6.57542E+0 | 6 | 2.175637 | 2.50102E+0 | 6 |
| 2.163463 | 6.44730E+0 | 6 | 2.175726 | 2.42110E+0 | 2 |
| 2.163548 | 6.42830E+0 | 2 | 2.175757 | 2.39647E+0 | 6 |
| 2.163759 | 6.34400E+0 | 3 | 2.175873 | 2.28530E+0 | 2 |
| 2.164086 | 6.32429E+0 | 6 | 2.175873 | 2.29089E+0 | 6 |
| 2.164086 | 6.32941E+0 | 6 | 2.175965 | 2.19915E+0 | 6 |
| 2.164859 | 6.16542E+0 | 6 | 2.175982 | 2.17940E+0 | 2 |
| 2.165154 | 6.10070E+0 | 2 | 2.176020 | 2.14431E+0 | 6 |
| 2.165684 | 5.99373E+0 | 6 | 2.176052 | 2.11151E+0 | 6 |
| 2.166426 | 5.82716E+0 | 6 | 2.176092 | 2.06150E+0 | 2 |
| 2.166576 | 5.79100E+0 | 2 | 2.176134 | 2.01360E+0 | 2 |
| 2.167091 | 5.67341E+0 | 6 | 2.176173 | 1.97109E+0 | 6 |
| 2.167334 | 5.61191E+0 | 6 | 2.176176 | 1.96400E+0 | 2 |
| 2.167822 | 5.49940E+0 | 2 | 2.176282 | 1.83476E+0 | 6 |
| 2.168334 | 5.37105E+0 | 6 | 2.176309 | 1.79320E+0 | 2 |
| 2.168924 | 5.21570E+0 | 2 | 2.176312 | 1.79069E+0 | 6 |
| 2.169001 | 5.19167E+0 | 6 | 2.176370 | 1.70920E+0 | 6 |
Table 4.1. (Continued)
T90 (K) |
u2 (m/s) |
Key |
T90 |
u2 (m/s) |
Key |
| 2.169524 | 5.05328E+0 | 6 | 2.176405 | 1.64980E+0 | 2 |
| 2.169730 | 4.99384E+0 | 6 | 2.176416 | 1.63489E+0 | 6 |
| 2.176478 | 1.52760E+0 | 2 | 2.176798 | 2.36555E-1 | 6 |
| 2.176492 | 1.50471E+0 | 6 | 2.176798 | 2.31385E-1 | 6 |
| 2.176495 | 1.49907E+0 | 6 | 2.176798 | 2.31731E-1 | 6 |
| 2.176521 | 1.44833E+0 | 6 | 2.176798 | 2.25518E-1 | 6 |
| 2.176533 | 1.42230E+0 | 2 | 2.176798 | 2.28820E-1 | 6 |
| 2.176576 | 1.33353E+0 | 6 | 2.176798 | 2.22728E-1 | 6 |
| 2.176576 | 1.33060E+0 | 2 | 2.176798 | 2.26967E-1 | 6 |
| 2.176587 | 1.30893E+0 | 6 | 2.176798 | 2.23868E-1 | 6 |
| 2.176590 | 1.29971E+0 | 6 | 2.176798 | 2.23047E-1 | 6 |
| 2.176610 | 1.24990E+0 | 2 | 2.176798 | 2.19049E-1 | 6 |
| 2.176614 | 1.24231E+0 | 6 | 2.176798 | 2.20092E-1 | 6 |
| 2.176625 | 1.21207E+0 | 6 | 2.176798 | 2.21236E-1 | 6 |
| 2.176637 | 1.17840E+0 | 2 | 2.176798 | 2.18135E-1 | 6 |
| 2.176641 | 1.17056E+0 | 6 | 2.176798 | 2.17216E-1 | 6 |
| 2.176649 | 1.14596E+0 | 6 | 2.176798 | 2.17216E-1 | 6 |
| 2.176650 | 1.14391E+0 | 6 | 2.176798 | 2.17216E-1 | 6 |
| 2.176660 | 1.11521E+0 | 6 | 2.176798 | 2.17216E-1 | 6 |
| 2.176660 | 1.11828E+0 | 6 | 2.176798 | 2.15304E-1 | 6 |
| 2.176660 | 1.11490E+0 | 2 | 2.176798 | 2.14397E-1 | 6 |
| 2.176672 | 1.07626E+0 | 6 | 2.176798 | 2.13386E-1 | 6 |
| 2.176678 | 1.05750E+0 | 2 | 2.176798 | 2.13386E-1 | 6 |
| 2.176693 | 1.00600E+0 | 2 | 2.176798 | 2.12502E-1 | 6 |
| 2.176697 | 9.94256E-1 | 6 | 2.176798 | 2.12502E-1 | 6 |
| 2.176706 | 9.59200E-1 | 2 | 2.176798 | 2.10558E-1 | 6 |
| 2.176710 | 9.43007E-1 | 6 | 2.176798 | 2.08686E-1 | 6 |
| 2.176717 | 9.16500E-1 | 2 | 2.176798 | 2.07804E-1 | 6 |
| 2.176726 | 8.77500E-1 | 2 | 2.176798 | 2.07852E-1 | 6 |
| 2.176729 | 8.62034E-1 | 6 | 2.176798 | 2.07852E-1 | 6 |
| 2.176733 | 8.41800E-1 | 2 | 2.176798 | 2.05951E-1 | 6 |
| 2.176737 | 8.25000E-1 | 2 | 2.176798 | 2.05093E-1 | 6 |
| 2.176743 | 7.97461E-1 | 6 | 2.176799 | 1.97314E-1 | 6 |
| 2.176744 | 7.93200E-1 | 2 | 2.176799 | 1.94212E-1 | 6 |
| 2.176754 | 7.39040E-1 | 6 | 2.176799 | 1.94212E-1 | 6 |
| 2.176764 | 6.69348E-1 | 6 | 2.176799 | 1.95274E-1 | 6 |
| 2.176764 | 6.71398E-1 | 6 | 2.176799 | 1.92427E-1 | 6 |
| 2.176775 | 5.89418E-1 | 6 | 2.176799 | 1.91700E-1 | 6 |
| 2.176777 | 5.65851E-1 | 6 | 2.176799 | 1.91700E-1 | 6 |
| 2.176785 | 4.83908E-1 | 6 | 2.176799 | 1.88324E-1 | 6 |
| 2.176788 | 4.51148E-1 | 6 | 2.176799 | 1.87355E-1 | 6 |
| 2.176792 | 3.82645E-1 | 6 | 2.176799 | 1.87355E-1 | 6 |
| 2.176795 | 3.24563E-1 | 6 | 2.176799 | 1.88426E-1 | 6 |
| 2.176797 | 2.72095E-1 | 6 | 2.176799 | 1.84011E-1 | 6 |
| 2.176797 | 2.66044E-1 | 6 | 2.176799 | 1.80988E-1 | 6 |
| 2.176797 | 2.61090E-1 | 6 | 2.176799 | 2.02214E-1 | 6 |
| 2.176797 | 2.48180E-1 | 6 | 2.176799 | 2.02434E-1 | 6 |
Table 4.1. (Continued)
T90 (K) |
u2 (m/s) |
Key |
T90 |
u2 (m/s) |
Key |
| 2.176798 | 2.42206E-1 | 6 | 2.176799 | 2.01435E-1 | 6 |
| 2.176798 | 2.36261E-1 | 6 | 2.176799 | 2.01435E-1 | 6 |
| 2.176798 | 2.35518E-1 | 6 | 2.176799 | 2.02490E-1 | 6 |
| 2.176799 | 1.99587E-1 | 6 | 2.176799 | 1.76016E-1 | 6 |
| 2.176799 | 1.98775E-1 | 6 | 2.176799 | 1.72643E-1 | 6 |
| 2.176799 | 1.99832E-1 | 6 | 2.176799 | 1.73834E-1 | 6 |
| 2.176799 | 1.94911E-1 | 6 | 2.176799 | 1.69586E-1 | 6 |
| 2.176799 | 1.95192E-1 | 6 | 2.176799 | 1.70702E-1 | 6 |
| 2.176799 | 1.78538E-1 | 6 | 2.176799 | 1.67700E-1 | 6 |
| 2.176799 | 1.78538E-1 | 6 | 2.176799 | 1.67819E-1 | 6 |
| 2.176799 | 1.77168E-1 | 6 | 2.176800 | 0.00000 | 0 |
| 2.176799 | 1.77211E-1 | 6 |
Table 4.2. Knots and coefficients for the spline fit for the velocity of second sound. The spline returns the velocity in m/s.
Knots |
Coefficients |
| K(1) = 0.5517426 | C(1)=1.050000E+02 |
| K(2) = 0.5517426 | C(2)=9.287425E+01 |
| K(3) = 0.5517426 | C(3)=4.973642E+01 |
| K(4) = 0.5517426 | C(4)=2.712778E+01 |
| K(5) = 0.6419700 | C(5)=1.931258E+01 |
| K(6) = 0.8062300 | C(6)=1.795336E+01 |
| K(7) = 0.9297000 | C(7)=1.923863E+01 |
| K(8) = 1.069640 | C(8)=2.115625E+01 |
| K(9) = 1.285500 | C(9)=1.921708E+01 |
| K(10) = 1.720200 | C(10)=1.575245E+01 |
| K(11) = 1.940430 | C(11)=1.192157E+01 |
| K(12) = 2.068850 | C(12)=8.953388E+00 |
| K(13) = 2.126220 | C(13)=6.771458E+00 |
| K(14) = 2.153079 | C(14)=5.506380E+00 |
| K(15) = 2.164207 | C(15)=4.456879E+00 |
| K(16) = 2.169182 | C(16)=3.840343E+00 |
| K(17) = 2.170551 | C(17)=2.542421E+00 |
| K(18) = 2.174832 | C(18)=1.957438E+00 |
| K(19) = 2.175738 | C(19)=1.427086E+00 |
| K(20) = 2.176319 | C(20)=1.001273E+00 |
| K(21) = 2.176600 | C(21)=6.743104E-01 |
| K(22) = 2.176735 | C(22)=4.565972E-01 |
| K(23) = 2.176780 | C(23)=3.519492E-01 |
| K(24) = 2.176787 | C(24)=2.088277E-01 |
| K(25) = 2.176797 | C(25)=1.059874E-01 |
| K(26) - K(29) | C(26)=0.000000E+00 |
| = 2.176800 |
Figure 4.1. The recommended values for the velocity of second sound in helium II as a function of temperature at saturated vapor pressure.