<<Previous

Intro

ch1

ch2

ch3

ch4

ch5

ch6

ch7

ch8

ch9

ch10

Next>>

ch11

ch12

ch13

ch14

ch15

ch16

ch17

ch18

ch19

ch20

ch21

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	D. F. Brewer and D. O. Edwards, “The Heat Conductivity and Viscosity of Liquid Helium II,” Proc. Roy. Soc. A 251, 247-264 (1959).
8	D. M. Lee and H. A. Fairbank, “Heat Transport in Liquid 3He,” Phys. Rev. 116, 1359 (1959).
9	G. Ahlers, “Thermal Conductivity of Helium I Near T Lambda,” in Eleventh International Conference on Low Temperature Physics (1968), Vol. 1, pp. 203-206.
10	G. Ahlers, “Thermal Conductivity of Helium I Near the Superfluid Transition,” Phys. Rev. Lett. 21, 1159-1162 (1968).
11	M. Archibald, J. M. Mochel, and L. Weaver, “Size Dependence of the Thermal Conductivity of Helium I Near the Lambda Point,” Phys. Rev. Lett. 21.16, 1156-1158 (1968).
12	J. F. Kerrisk, “The Thermal Conductivity of Liquid Helium II and Liquid 3He,” Ph.D. Thesis, Univ. of New Mexico, 1968 (unpublished).
13	J. Kerrisk and W. Keller, “Thermal Conductivity of Fluid 3He and 4He of Temperatures Between 1.5 and 4.0 Degrees K and for Pressures up to 34 atm.,” Phys. Rev. 177.1, 341-351 (1969).
14	M. Tanaka and A. Ikushima, “Thermal Transport Phenomena Near the Lambda Line of 3He 4He Mixtures,” J. Low Temp. Phys. 35, 9-23 (1979).
15	A. Acton and K. Kellner, “The Low Temperature Thermal Conductivity of 4He,” Physica B 103, 212-225 (1981).
16	G. Ahlers, P. C. Hohenberg, and A. Kornblit, “Critical Thermal Conductivity of 4He for T >= T Lambda,” Phys. Rev. Lett. 46, 493-496 (1981).
17	G. Ahlers, P. C. Hohenberg, and A. Kornblit, “Nonlinear Renormalization-Group Analysis of the Thermal Conductivity of 4He for T >= T Lambda,” Phys. Rev. B 25, 3136-3167 (1982).
18	D. Gestrich, M. Dingus, and H. Meyer, “Thermal Conductivity of Dilute 3He-4He Mixtures Near the Superfluid Transition,” Phys. Lett. 99A, 331-334 (1983).
19	W. Y. Tam, “Thermal Conductivity of 4He-I Near the Superfluid Transition,” Ph.D. Thesis, University of California, Santa Barbara, 1985.
20	W. Y. Tam and G. Ahlers, “Thermal Conductivity of 4He I from near T?to 3.6K and Vapor Pressure to 30 bar,” Phys. Rev. B 32, 5932 (1985).
21	. M. Dingus, F. Zhong, and H. Meyer, “Thermal Transport Properties in Helium near the Superfluid Transition: (I) 4He in the Normal Phase,” J. Low Temp. Phys. 65, 185 (1986)