|
|
The
Observed Properties of Liquid Helium
at the Saturated Vapor
Pressure
Chapter
14. Structure Factor
Adopted Database
Author(s) |
Key # |
Range(Å-1) |
Ahlers |
1 |
2.172
T
2.176 |
Behringer
& Ahlers |
2 |
2.1728
T
4.209 |
Tam
& Ahlers |
3 |
2.172
T
2.542 |
Dingus,
Zhong & Meyer |
4 |
2.172
T
3.765 |
Comments
and Key to Authors
1)
Ref. 10. Uncertainties as in note 3. Systematic uncertainties increase
below .
2) Quoted in Ref. 17. Uncertainties: T/T-1>10-5roughly
0.1%. Otherwise uncertainties rise closer to T
and a formula given.
3) Ref. 20. Uncertainties:T/T-1>10-5
, , otherwise 0.1%.
4) Ref. 21. Table IV only. Uncertainty: < 5%.
5) To convert from mW/cm-K to erg/cm-s-K multiply by 104.
Table
15.1. Adopted database for the thermal conductivity of liquid 4He.
T90 (K) |
k(mW/cm K) |
Key |
T90 (K) |
k(mW/cm K) |
Key |
2.176804 |
4.46684E0 |
1 |
2.176821 |
2.23872E0
|
1 |
2.176805 |
4.16869E0
|
1 |
2.176821
|
1.89150E0 |
3 |
2.176806
|
3.40400E0
|
4
|
2.176823
|
2.13796E0 |
1 |
2.176807 |
3.30560E0
|
3
|
2.176823
|
1.89220E0
|
4 |
2.176807
|
3.63078E0
|
1 |
2.176824 |
1.79140E0 |
3 |
2.176807 |
3.02850E0 |
3 |
2.176826
|
1.75310E0 |
3 |
2.176807 |
3.08450E0 |
4 |
2.176828
|
1.99526E0 |
1 |
2.176808
|
3.09780E0 |
3 |
2.176829 |
1.69580E0 |
4 |
2.176808 |
2.92100E0
|
4
|
2.176831 |
1.73780E0 |
1 |
2.176808
|
2.76410E0 |
3
|
2.176832 |
1.59030E0
|
3 |
2.176808
|
3.31131E0
|
1 |
2.176833 |
1.58120E0 |
3 |
2.176809 |
3.01995E0 |
1 |
2.176833 |
1.73780E0 |
1 |
2.176810
|
2.68100E0 |
4 |
2.176836 |
1.56380E0 |
4 |
2.176810
|
2.62770E0 |
3 |
2.176841
|
1.41910E0
|
3 |
2.176812 |
2.35640E0 |
3 |
2.176841
|
1.51356E0 |
1 |
2.176812
|
2.39600E0
|
4 |
2.176842 |
1.41860E0
|
3 |
2.176812 |
2.41710E0 |
3
|
2.176846 |
1.51356E0 |
1 |
2.176813 |
2.75423E0
|
1
|
2.176846
|
1.37400E0 |
4 |
2.176813 |
2.33220E0 |
3 |
2.176850
|
1.33330E0
|
4 |
2.176814
|
2.32110E0 |
4 |
2.176851 |
1.44544E0 |
1 |
2.176814 |
2.69153E0 |
1 |
2.176854
|
1.27540E0 |
3 |
2.176815
|
2.25610E0
|
3 |
2.176854
|
1.23990E0 |
3 |
2.176816
|
2.51189E0
|
1
|
2.176856
|
1.38038E0
|
1 |
2.176816 |
2.10000E0
|
3 |
2.176863 |
1.19050E0
|
4 |
2.176817
|
2.13140E0 |
4 |
2.176863
|
1.14640E0 |
3 |
2.176818 |
2.34423E0 |
1 |
2.176866 |
1.31826E0 |
1 |
2.176820 |
1.95900E0 |
4 |
2.176868
|
1.14680E0
|
3 |
2.176820 |
1.93570E0
|
3
|
2.176872
|
1.25893E0 |
1 |
2.176876 |
1.09400E0 |
4 |
2.177126 |
5.77800E-1 |
3 |
2.176881 |
1.06730E0 |
3 |
2.177128
|
5.71000E-1 |
3 |
2.176882 |
1.02910E0 |
3 |
2.177145 |
5.70700E-1 |
4 |
2.176883
|
1.14815E0 |
1 |
2.177152 |
6.02560E-1 |
1 |
2.176889 |
1.03250E0
|
4
|
2.177169
|
5.88844E-1
|
1 |
2.176893
|
1.07152E0 |
1 |
2.177173 |
5.43890E-1
|
4 |
2.176894 |
9.96800E-1 |
3
|
2.177199 |
5.23600E-1 |
3 |
2.176896 |
9.67000E-1 |
3 |
2.177204 |
5.49541E-1 |
1 |
2.176899 |
1.07152E0 |
1
|
2.177230
|
5.11800E-1
|
3 |
2.176911
|
9.50500E-1 |
4 |
2.177249 |
4.93400E-1 |
3 |
2.176917 |
8.78200E-1 |
3 |
2.177264 |
5.37032E-1
|
1 |
2.176921
|
9.03500E-1
|
3 |
2.177296
|
4.80700E-1
|
3 |
2.176925
|
8.85390E-1
|
4
|
2.177305
|
4.80550E-1 |
4 |
2.176937
|
9.12011E-1 |
1
|
2.177309 |
5.24807E-1 |
1 |
2.176943 |
8.06900E-1 |
3 |
2.177333 |
4.89779E-1
|
1 |
2.176947 |
8.51138E-1 |
1 |
2.177346 |
4.51000E-1 |
3 |
2.176960 |
8.03900E-1 |
4
|
2.177441 |
4.57088E-1 |
1 |
2.176963
|
7.87700E-1 |
3
|
2.177468 |
4.23100E-1 |
3 |
Table 15.1. (Continued)
T90 (K) |
k(mW/cm K) |
Key |
T90 (K) |
k(mW/cm K) |
Key |
2.176973 |
8.31764E-1 |
1 |
2.177498 |
4.13500E-1
|
4 |
2.176974 |
7.42300E-1 |
3 |
2.177499
|
4.07500E-1
|
3 |
2.176978 |
7.55400E-1 |
3 |
2.177500 |
4.17800E-1
|
4 |
2.177010
|
7.03600E-1 |
4 |
2.177553 |
4.16869E-1 |
1 |
2.177022 |
7.07946E-1 |
1 |
2.177634
|
3.84583E-1 |
2 |
2.177049
|
6.61700E-1 |
4 |
2.177647
|
3.84350E-1
|
4 |
2.177050 |
6.50000E-1 |
3
|
2.177649
|
3.82300E-1 |
3 |
2.177061
|
6.76083E-1 |
1 |
2.177665 |
3.98107E-1 |
1 |
2.177093
|
6.30957E-1 |
1 |
2.177726 |
3.64100E-1 |
3 |
2.177096
|
6.02200E-1 |
4 |
2.177802
|
3.57800E-1
|
3 |
2.177824
|
3.56200E-1 |
4
|
2.180894
|
2.15900E-1
|
3 |
2.177881
|
3.47680E-1
|
4
|
2.180918 |
2.16000E-1 |
4 |
2.177918 |
3.40400E-1 |
3 |
2.180939
|
2.29087E-1 |
1 |
2.177966
|
3.54813E-1 |
1
|
2.181006
|
2.16576E-1 |
2 |
2.178076
|
3.23800E-1
|
3
|
2.181598
|
2.08100E-1 |
4 |
2.178174
|
3.13800E-1 |
3 |
2.181708 |
2.05500E-1
|
3 |
2.178264 |
3.09030E-1 |
4
|
2.181712 |
2.06700E-1 |
3 |
2.178506
|
2.90600E-1 |
3 |
2.182109 |
2.00800E-1
|
4 |
2.178595
|
2.84000E-1 |
4 |
2.182148 |
2.00200E-1 |
3 |
2.178606 |
2.81500E-1 |
3 |
2.182532 |
1.95700E-1
|
3 |
2.178781
|
2.95121E-1
|
1
|
2.182761
|
1.95100E-1 |
4 |
2.178813
|
2.73000E-1 |
3
|
2.183106
|
1.91400E-1 |
4 |
2.178860
|
2.72446E-1 |
2 |
2.184050 |
1.85200E-1 |
3 |
2.178987
|
2.65600E-1 |
3 |
2.184066 |
1.86400E-1 |
4 |
2.179120 |
2.58400E-1 |
3
|
2.184706 |
1.83600E-1 |
3 |
2.179127 |
2.75423E-1 |
1
|
2.184832
|
1.83227E-1 |
2 |
2.179463
|
2.49500E-1 |
4
|
2.185046 |
1.81100E-1 |
4 |
2.179606 |
2.45200E-1 |
3 |
2.186237
|
1.76600E-1 |
3 |
2.179789 |
2.39200E-1 |
4 |
2.186423
|
1.75100E-1
|
4 |
2.179993
|
2.32900E-1 |
3
|
2.186423 |
1.76300E-1 |
4 |
2.180049 |
2.32600E-1 |
4 |
2.186858
|
1.73800E-1 |
3 |
2.180067 |
2.31200E-1 |
4
|
2.188800 |
1.69100E-1 |
3 |
2.180112
|
2.32200E-1 |
4 |
2.188855
|
1.69594E-1
|
2 |
2.180147
|
2.31800E-1
|
4
|
2.189593
|
1.65200E-1 |
4 |
2.180242
|
2.34423E-1 |
1
|
2.190521
|
1.64200E-1
|
3 |
2.180253
|
2.29300E-1
|
4
|
2.190657
|
1.65500E-1 |
3 |
2.180263 |
2.28400E-1 |
3 |
2.192880 |
1.61689E-1 |
2 |
2.180330 |
2.27800E-1 |
4 |
2.192923
|
1.60800E-1
|
4 |
2.196183 |
1.56400E-1 |
4
|
2.259352 |
1.41600E-1
|
3 |
2.196908
|
1.56715E-1
|
2
|
2.259664
|
1.41100E-1 |
4 |
2.197991 |
1.55400E-1 |
3
|
2.272133
|
1.41300E-1 |
3 |
2.199452
|
1.51500E-1 |
4 |
2.276905 |
1.40600E-1 |
4 |
2.200223 |
1.52800E-1
|
3 |
2.287034 |
1.41300E-1 |
3 |
2.200336 |
1.53300E-1 |
3 |
2.289631
|
1.41814E-1 |
2 |
2.202731
|
1.52100E-1
|
4
|
2.312101
|
1.41100E-1 |
4 |
2.203281 |
1.51939E-1 |
2 |
2.327997 |
1.42300E-1 |
3 |
Table
15.1. (Continued)
T90 (K) |
k(mW/cm K) |
Key |
T90 (K) |
k(mW/cm K) |
Key |
2.206011 |
1.49300E-1 |
4 |
2.331968 |
1.43077E-1 |
2 |
2.206011
|
1.49500E-1 |
4 |
2.331969 |
1.42870E-1 |
2 |
2.206109
|
1.48900E-1
|
3
|
2.348300
|
.42500E-1 |
4 |
2.209292
|
1.48100E-1
|
4 |
2.369424 |
1.43600E-1 |
3 |
2.209292
|
1.49600E-1 |
4 |
2.375205
|
1.44787E-1 |
2 |
2.209381
|
1.48300E-1 |
3 |
2.385618 |
1.44100E-1
|
4 |
2.211370 |
1.48112E-1 |
2 |
2.402033
|
1.45100E-1 |
3 |
2.214110 |
1.46700E-1 |
3 |
2.419273 |
1.46497E-1 |
2 |
2.215896 |
1.44900E-1 |
4
|
2.463775
|
1.45100E-1
|
4 |
2.216593 |
1.44000E-1 |
3 |
2.479577 |
1.48400E-1
|
3 |
2.219484 |
1.45952E-1 |
2 |
2.487082
|
1.49748E-1 |
2 |
2.225869 |
1.43300E-1 |
4 |
2.533625 |
1.51943E-1 |
2 |
2.227626
|
1.44434E-1
|
2 |
2.547352 |
1.49900E-1 |
4 |
2.228390 |
1.43700E-1 |
3 |
2.562433 |
1.52200E-1 |
3 |
2.233576
|
1.43200E-1
|
3
|
2.629982 |
1.56950E-1 |
2 |
2.235797 |
1.43430E-1 |
2
|
2.638230 |
1.55600E-1 |
3 |
2.242645
|
1.42900E-1 |
4 |
2.731245 |
1.61711E-1
|
2 |
2.242667 |
1.42100E-1 |
4 |
2.731339
|
21.61812E-1
|
2 |
2.243996 |
1.42725E-1 |
2 |
2.772403 |
1.61100E-1
|
3 |
2.248106
|
1.42620E-1 |
2
|
2.838136 |
1.66613E-1
|
2 |
2.838136
|
1.66491E-1 |
2
|
3.643302
|
1.92895E-1
|
2 |
2.920833 |
1.67000E-1 |
3 |
3.772385
|
1.88500E-1 |
3 |
3.010123 |
1.73672E-1 |
2 |
3.772385
|
1.88500E-1 |
3 |
3.085844 |
1.72500E-1 |
3
|
3.816934
|
1.95957E-1 |
2 |
3.133917 |
1.78308E-1
|
2
|
3.909782 |
1.97274E-1 |
2 |
3.300888
|
1.84115E-1
|
2
|
4.006976 |
1.98148E-1 |
2 |
3.421077 |
1.81900E-1 |
3 |
4.109041
|
1.98852E-1 |
2 |
3.483569 |
1.89601E-1
|
2
|
4.216445
|
1.99402E-1
|
2 |
3.588699
|
1.85500E-1 |
3 |
|
|
|
Figure 15.1. The recommended
values for the thermal conductivity of liquid 4He as a function of temperature
at the saturated vapor pressure.
Table
15.2. Knots and coefficients for the spline fit of thermal conductivity.
This spline returns the conductivity in W/m-K.
Knots |
Coefficients |
K(1)
= 2.176804 |
C(1)
= 4.467094E-1 |
K(2)
= 2.176804 |
C(2)
= 4.079579E-1 |
K(3)
= 2.176804 |
C(3)
= 2.734695E-1 |
K(4)
= 2.176804 |
C(4)
= 1.932048E-1 |
K(5)
= 2.176806 |
C(5)
= 1.266490E-1 |
K(6)
= 2.176814 |
C(6)
= 7.907832E-2 |
K(7)
= 2.176841 |
C(7)
= 6.252596E-2 |
K(8)
= 2.176890 |
C(8)
= 4.624502E-2 |
K(9)
= 2.177066 |
C(9) = 3.358313E-2 |
K(10)
= 2.177250 |
C(10)
= 2.422696E-2 |
K(11)
= 2.177640 |
C(11)
= 1.775809E-2 |
K(12)
= 2.178583 |
C(12)
= 1.549755E-2 |
K(13)
= 2.181366 |
C(13)
= 1.398263E-2 |
K(14)
= 2.190463 |
C(14)
= 1.416969E-2 |
K(15)
= 2.209490 |
C(15)
= 1.783677E-2 |
K(16)
= 2.290049 |
C(16)
= 1.926469E-2 |
K(17)
= 2.550721 |
C(17)
= 1.994140E-2 |
K(18)
= 4.216445 |
|
K(19)
= 4.216445 |
|
K(20)
= 4.216445 |
|
K(21)
= 4.216445 |
|
Figure
15.2. Log plot of vs | T - T?
|..
Figure 15.3. Deviation of the
database from the spline fit of thermal conductivity expressed in percent.
Table
15.3. Recommended values of thermal conductivity in helium I.
T90
(K) |
k(mW/cm K) |
T90
(K) |
k(mW/cm K) |
2.17681 |
2.6979 |
2.75 |
0.1617 |
2.17682
|
2.0756 |
2.80 |
0.1639 |
2.17683 |
1.7337
|
2.85 |
0.1659 |
2.17684 |
1.5163 |
2.90 |
0.1679 |
2.17685
|
1.3609 |
2.95 |
0.1699 |
2.17686 |
1.2451 |
3.00 |
0.1717 |
2.17687
|
1.1600 |
3.05 |
0.1735 |
2.17688
|
1.0968 |
3.10 |
0.1753 |
2.17689
|
1.0463
|
3.15
|
0.1769 |
2.1769 |
1.0014 |
3.20
|
0.1785 |
2.1770
|
0.7287
|
3.25 |
0.1800 |
2.1775 |
0.4205 |
3.30
|
0.1815 |
2.1780
|
0.3337
|
3.35
|
0.1829 |
2.1785 |
0.2930 |
3.40 |
0.1843 |
2.1790 |
0.2678 |
3.45 |
0.1855 |
2.1795
|
0.2489
|
3.50 |
0.1868 |
2.1800 |
0.2354 |
3.55 |
0.1880 |
2.1850 |
0.1808 |
3.60 |
0.1891 |
2.1900
|
0.1647 |
3.65 |
0.1902 |
2.1950 |
0.1578 |
3.70 |
0.1912 |
2.20 |
0.1534 |
3.75
|
0.1922 |
2.25
|
0.1413
|
3.80 |
0.1931 |
2.30 |
0.1413 |
3.85 |
0.1940 |
2.35 |
0.1429
|
3.90 |
0.1949 |
2.40
|
0.1449
|
3.95
|
0.1957 |
2.45 |
0.1472 |
4.00 |
0.1965 |
2.50
|
0.1497 |
4.05 |
0.1972 |
2.55 |
0.1523 |
4.10 |
0.1979 |
2.60 |
0.1548 |
4.15
|
0.1986 |
2.65
|
0.1572
|
4.20 |
0.1992 |
2.70 |
0.1595 |
|
|
Chronological Bibliography for Mutual Friction
1 |
W. H. Keesom and A. P. Keesom, "On the Heat Conductivity of Liquid
Helium," Physica 3, 359-360 (1936). |
2 |
P.
L. Kapitza, “The Study of Heat Transfer in Helium II,”
J. Phys. USSR 4, 181-210 (1941). |
3 |
C.
Grenier, “Thermal Conductivity of Liquid Helium I,” Phys.
Rev. 83, 598-603 (1951). |
4 |
R.
Bowers, “The Thermal Conductivity of Liquid Helium I,”
Proc. Phys. Soc. LXV 7A, 511-518 (1952). |
5 |
C.
J. Challis and J. Wilks, “U. S. Air Force Office of Scientific
Research Report No. TR-57-78,” in The Symposium on Solid and
Liquid Helium 3 (Ohio State Univ. Research Institute, Columbus, OH,
1957), Vol. 38. |
6 |
P.
Winkel and D. N. Wansink, “Transport Phenomena of Liquid Helium
II in Slits and Capillaries,” in Prog. in Low Temp. Physics,
edited by C. J. Gorter (Interscience Publishers, New York, 1957),
Vol. 2, pp. 83-104. |
7 |
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