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 8. Entropy
Adopted Database for µ+
Author(s) |
Key # |
Method |
Range (K) |
| Barenghi, et al. | 1 | Ion Pool | 0.2388
 T
0.8462 |
| Schwarz | 2 | Drift Velocity | 0.371
T
5.18
|
Adopted Database for µ-
Author(s) |
Key # |
Method |
Range (K) |
| Barenghi, et al. | 1 | Ion Pool | 0.0528
T
0.9632 |
| Schwarz | 2 | Drift Velocity | 0.247
T
5.18
|
Comments and Key to Authors
1) Ref. 18. Uncertainties: for negative ions, > 270mK, and for positive ions, > 370mK, results are in good agreement with Ref. 14. Below these temperatures the mobilities depend on the experimental situation and the paper should be consulted for details.
2) Ref. 14. Uncertainty better than 2%.
3) The splines are fit to the log10 of the mobility.
4) To convert mobilities from m2/V×s to cm2/V×s, multiply by 104.
Table 10.1. Adopted database for the positive ion mobility.
T90 (K) |
µ+(m2/V.s) |
Key |
T90 |
µ+(m2/V.s) |
Key |
| 0.0255 | 2.11000E+3 | 1 | 0.3953 | 3.80000E+0 | 2 |
| 0.0421 | 1.73000E+3 | 1 | 0.4020 | 4.97000E+0 | 1 |
| 0.0459 | 1.38000E+3 | 1 | 0.4063 | 3.36000E+0 | 2 |
| 0.0599 | 1.32000E+3 | 1 | 0.4108 | 4.01000E+0 | 1 |
| 0.0656 | 1.22000E+3 | 1 | 0.4124 | 2.95000E+0 | 2 |
| 0.0736 | 1.05000E+3 | 1 | 0.4214 | 2.63000E+0 | 2 |
| 0.0836 | 1.10000E+3 | 1 | 0.4216 | 4.18000E+0 | 1 |
| 0.0850 | 9.13000E+2 | 1 | 0.4304 | 2.38000E+0 | 2 |
| 0.0922 | 9.45000E+2 | 1 | 0.4326 | 2.86000E+0 | 1 |
| 0.1037 | 8.46000E+2 | 1 | 0.4404 | 2.05000E+0 | 2 |
| 0.1052 | 7.75000E+2 | 1 | 0.4502 | 2.17000E+0 | 1 |
| 0.1103 | 7.70000E+2 | 1 | 0.4515 | 1.75000E+0 | 2 |
| 0.1250 | 5.96000E+2 | 1 | 0.4525 | 3.51000E+0 | 1 |
| 0.1259 | 6.51000E+2 | 1 | 0.4525 | 3.61000E+0 | 1 |
| 0.1259 | 5.71000E+2 | 1 | 0.4525 | 2.83000E+0 | 1 |
| 0.1479 | 4.21000E+2 | 1 | 0.4625 | 1.46000E+0 | 2 |
| 0.1505 | 4.10000E+2 | 1 | 0.4731 | 1.68000E+0 | 1 |
| 0.1560 | 3.95000E+2 | 1 | 0.4735 | 1.23000E+0 | 2 |
| 0.1636 | 2.85000E+2 | 1 | 0.4856 | 1.01000E+0 | 2 |
| 0.1688 | 3.06000E+2 | 1 | 0.4893 | 1.15000E+0 | 1 |
| 0.1740 | 2.14000E+2 | 1 | 0.4996 | 8.05000E-1 | 2 |
| 0.1790 | 2.07000E+2 | 1 | 0.5073 | 9.81000E-1 | 1 |
| 0.1865 | 1.56000E+2 | 1 | 0.5116 | 6.42000E-1 | 2 |
| 0.1865 | 1.82000E-+2 | 1 | 0.5253 | 7.32000E-1 | 1 |
| 0.1889 | 1.76000E+2 | 1 | 0.5277 | 4.86000E-1 | 2 |
| 0.1988 | 1.43000E+2 | 1 | 0.5310 | 6.81000E-1 | 1 |
| 0.2059 | 1.42000E+2 | 1 | 0.5417 | 3.73000E-1 | 2 |
| 0.2181 | 9.22000E+1 | 1 | 0.5470 | 5.02000E-1 | 1 |
| 0.2227 | 9.02000E+1 | 1 | 0.5501 | 4.86000E-1 | 1 |
| 0.2390 | 6.17000E+1 | 1 | 0.5568 | 2.76000E-1 | 2 |
| 0.2454 | 4.35000E+1 | 1 | 0.5679 | 3.45000E-1 | 1 |
| 0.2627 | 3.74000E+1 | 1 | 0.5718 | 3.28000E-1 | 1 |
| 0.2687 | 2.93000E+1 | 1 | 0.5748 | 1.98000E-1 | 2 |
| 0.2816 | 2.50000E+1 | 1 | 0.5883 | 2.04000E-1 | 1 |
| 0.3012 | 1.70000E+1 | 1 | 0.5917 | 2.19000E-1 | 1 |
| 0.3039 | 1.53000E+1 | 1 | 0.5918 | 2.25000E-1 | 1 |
| 0.3063 | 2.29000E+1 | 1 | 0.5918 | 1.41000E-1 | 2 |
| 0.3313 | 1.07000E+1 | 1 | 0.6115 | 1.55000E-1 | 1 |
| 0.3318 | 1.00000E+1 | 1 | 0.6117 | 1.32000E-1 | 1 |
| 0.3522 | 8.03000E+0 | 1 | 0.6119 | 9.65000E-2 | 2 |
| 0.3569 | 8.02000E+0 | 1 | 0.6121 | 1.49000E-2 | 1 |
| 0.3702 | 6.50000E+0 | 1 | 0.6218 | 1.25000E-2 | 1 |
| 0.3703 | 6.71000E+0 | 1 | 0.6330 | 6.60000E-2 | 2 |
| 0.3722 | 5.19000E+0 | 2 | 0.6340 | 8.76000E-2 | 1 |
| 0.3793 | 4.72000E+0 | 2 | 0.6371 | 9.54000E-2 | 1 |
| 0.3873 | 4.18000E+0 | 2 | 0.6440 | 8.27000E-2 | 1 |
| 0.3917 | 5.02000E+0 | 1 | 0.6508 | 7.48000E-2 | 1 |
Table 10.1. (Continued)
T90 (K) |
µ+(m2/V.s) |
Key |
T90 |
µ+(m2/V.s) |
Key |
| 0.6550 | 4.45000E-2 | 2 | 0.9788 | 8.09000E+0 | 1 |
| 0.6599 | 6.24000E-2 | 1 | 0.9988 | 7.15000E-4 | 2 |
| 0.6648 | 5.83000E-2 | 1 | 1.0026 | 6.44000E-4 | 1 |
| 0.6781 | 2.97000E-2 | 2 | 1.0218 | 5.60000E-4 | 1 |
| 0.6784 | 4.59000E-2 | 1 | 1.0509 | 4.80000E-4 | 2 |
| 0.6788 | 3.96000E-2 | 1 | 1.1350 | 2.57000E-4 | 2 |
| 0.6845 | 4.23000E-2 | 1 | 1.1991 | 1.66000E-4 | 2 |
| 0.6910 | 3.22000E-2 | 1 | 1.3003 | 9.16000E-5 | 2 |
| 0.6947 | 3.50000E-2 | 1 | 1.4015 | 5.48000E-5 | 2 |
| 0.6972 | 3.36000E-2 | 1 | 1.5036 | 3.53000E-5 | 2 |
| 0.7031 | 2.03000E-2 | 2 | 1.6057 | 2.44000E-5 | 2 |
| 0.7038 | 2.97000E-2 | 1 | 1.7119 | 1.80000E-5 | 2 |
| 0.7108 | 2.70000E-2 | 1 | 1.8161 | 1.39000E-5 | 2 |
| 0.7154 | 2.18000E-2 | 1 | 1.9172 | 1.09000E-5 | 2 |
| 0.7213 | 2.25000E-2 | 1 | 2.0203 | 8.42000E-6 | 2 |
| 0.7292 | 1.38000E-2 | 2 | 2.1215 | 6.22000E-6 | 2 |
| 0.7318 | 1.65000E-2 | 1 | 2.1365 | 5.86000E-6 | 2 |
| 0.7330 | 1.93000E-2 | 1 | 2.1516 | 5.55000E-6 | 2 |
| 0.7402 | 1.69000E-2 | 1 | 2.1676 | 5.17000E-6 | 2 |
| 0.7474 | 1.54000E-2 | 1 | 2.1738 | 5.04000E-6 | 2 |
| 0.7505 | 1.25000E-2 | 1 | 2.1788 | 4.96000E-6 | 2 |
| 0.7591 | 1.31000E-2 | 1 | 2.2046 | 4.72000E-6 | 2 |
| 0.7593 | 8.86000E-3 | 2 | 2.2647 | 4.52000E-6 | 2 |
| 0.7633 | 1.22000E-2 | 1 | 2.3749 | 4.30000E-6 | 2 |
| 0.7637 | 1.19000E-2 | 1 | 2.4951 | 4.20000E-6 | 2 |
| 0.7715 | 9.20000E-3 | 1 | 2.6455 | 4.13000E-6 | 2 |
| 0.7731 | 1.07000E-2 | 1 | 2.8260 | 4.12000E-6 | 2 |
| 0.7833 | 8.98000E-3 | 1 | 3.0263 | 4.16000E-6 | 2 |
| 0.7877 | 8.52000E=3 | 1 | 3.2567 | 4.23000E-6 | 2 |
| 0.7883 | 6.05000E-3 | 2 | 3.5070 | 4.35000E-2 | 2 |
| 0.7928 | 6.78000E-3 | 1 | 3.7771 | 4.49000E-2 | 2 |
| 0.8070 | 6.44000E-3 | 1 | 3.9370 | 4.60000E-2 | 2 |
| 0.8107 | 5.29000E-3 | 1 | 4.1671 | 4.70000E-2 | 2 |
| 0.8224 | 4.01000E-3 | 2 | 4.3370 | 4.80000E-2 | 2 |
| 0.8324 | 3.93000E-3 | 1 | 4.4570 | 4.87000E-2 | 2 |
| 0.8543 | 2.98000E-3 | 1 | 4.5571 | 4.98000E-2 | 2 |
| 0.8615 | 2.58000E-3 | 2 | 4.7073 | 4.97000E-2 | 2 |
| 0.8761 | 2.39000E-3 | 1 | 4.8473 | 4.92000E-6 | 2 |
| 0.8821 | 2.20000E-3 | 1 | 4.9673 | 4.89000E-6 | 2 |
| 0.8914 | 1.96000E-3 | 1 | 5.0172 | 4.83000E-6 | 2 |
| 0.8996 | 1.74000E-3 | 2 | 5.0571 | 4.73000E-6 | 2 |
| 0.9131 | 1.55000E-3 | 1 | 5.0871 | 4.62000E-6 | 2 |
| 0.9344 | 1.24000E-3 | 1 | 5.1270 | 4.47000E-6 | 2 |
| 0.9477 | 1.11000E-3 | 2 | 5.1669 | 4.01000E-6 | 2 |
| 0.9541 | 1.04000E-3 | 1 | 5.1868 | 3.76000E-6 | 2 |
Figure 10.1. Positive ion mobility as a function of temperature along the saturated vapor pressure line.
Table 10.2. Knots and coefficients for the spline fit of .
Knots |
Coefficients |
| K(1) = 2.549509E-2 | C(1) = 7.324336E-4 |
| K(2) = 2.549509E-2 | C(2) = 7.127592E-4 |
| K(3) = 2.549509E-2 | C(3) = 6.936548E-4 |
| K(4) = 2.549509E-2 | C(4) = 5.173557E-4 |
| K(5) = 8.989802E-2 | C(5) = 4.285367E-4 |
| K(6) = 2.949869E-1 | C(6) = 2.823892E-4 |
| K(7) = 4.513886E-1 | C(7) = 2.125491E-4 |
| K(8) = 7.045304E-1 | C(8) = 1.285926E-4 |
| K(9) = 7.577476E-1 | C(9) = 5.123347E-5 |
| K(10) = 7.944735E-1 | C(10) = -3.728677E-5 |
| K(11) = 1.062780E+0 | C(11) = -8.564176E-5 |
| K(12) = 1.394506E+0 | C(12) = -1.067754E-4 |
| K(13) = 1.791246E+0 | C(13) = -1.321435E-4 |
| K(14) = 2.152366E+0 | C(14) = -1.381473E-4 |
| K(15) = 2.203504E+0 | C(15) = -1.396425E-4 |
| K(16) = 2.205589E+0 | C(16) = -1.325568E-4 |
| K(17) = 2.727358E+0 | C(17) = -1.292173E-4 |
| K(18) = 4.425492E+0 | C(18) = -1.335656E-4 |
| K(19) = 5.043800E+0 | C(19) = -1.409701E-4 |
| K(20) = 5.154401E+0 | C(20) = -1.424813E-4 |
| K(21) = 5.186798E+0 | |
| K(22) = 5.186798E+0 | |
| K(23) = 5.186798E+0 | |
| K(24) = 5.186798E+0 |
Figure 10.2. Deviation of the database from the spline fit to .
Note : The large deviations at low temperatures reflect a divergence in magnitudes reported in Refs. 14 and 18.
Table 10.3. Adopted database for the negative ion mobility.
T90 (K) |
µ-(m2/V.s) |
Key |
T90 |
µ-(m2/V.s) |
Key |
| 0.0351 | 1.08000E+3 | 1 | 0.0884 | 8.79000E+0 | 1 |
| 0.0405 | 6.47000E+2 | 1 | 0.0884 | 8.89000E+0 | 1 |
| 0.0449 | 3.76000E+2 | 1 | 0.0903 | 7.10000E+0 | 1 |
| 0.0496 | 2.49000E+2 | 1 | 0.0915 | 7.49000E+0 | 1 |
| 0.0531 | 1.69000E+2 | 1 | 0.0921 | 7.30000E+0 | 1 |
| 0.0541 | 1.34000E+2 | 1 | 0.0942 | 6.59000E+0 | 1 |
| 0.0541 | 1.46000E+2 | 1 | 0.0946 | 5.74000E+0 | 1 |
| 0.0547 | 1.41000E+2 | 1 | 0.0986 | 5.44000E+0 | 1 |
| 0.0547 | 1.29000E+2 | 1 | 0.0987 | 4.68000E+0 | 1 |
| 0.0555 | 1.18000E+2 | 1 | 0.0998 | 4.91000E+0 | 1 |
| 0.0560 | 1.16000E+2 | 1 | 0.1002 | 5.70000E+0 | 1 |
| 0.0575 | 9.48000E+1 | 1 | 0.1014 | 5.00000E+0 | 1 |
| 0.0578 | 8.71000E+1 | 1 | 0.1015 | 4.51000E+0 | 1 |
| 0.0596 | 7.91000E+1 | 1 | 0.1019 | 4.81000E+0 | 1 |
| 0.0596 | 7.72000E+1 | 1 | 0.1019 | 4.76000E+0 | 1 |
| 0.0596 | 8.11000E+1 | 1 | 0.1019 | 4.79000E+0 | 1 |
| 0.0597 | 7.72000E+1 | 1 | 0.1036 | 4.72000E+0 | 1 |
| 0.0597 | 7.80000E+1 | 1 | 0.1044 | 4.33000E+0 | 1 |
| 0.0597 | 7.83000E+1 | 1 | 0.1048 | 3.75000E+0 | 1 |
| 0.0601 | 7.41000E+1 | 1 | 0.1048 | 3.98000E+0 | 1 |
| 0.0601 | 7.02000E+1 | 1 | 0.1064 | 3.42000E+0 | 1 |
| 0.0601 | 7.18000E+1 | 1 | 0.1083 | 3.41000E+0 | 1 |
| 0.0601 | 6.87000E+1 | 1 | 0.1084 | 3.72000E+0 | 1 |
| 0.0616 | 6.01000E+1 | 1 | 0.1102 | 3.49000E+0 | 1 |
| 0.0621 | 6.22000E+1 | 1 | 0.1125 | 3.26000E+0 | 1 |
| 0.0622 | 5.99000E+1 | 1 | 0.1125 | 3.22000E+0 | 1 |
| 0.0632 | 5.59000E+1 | 1 | 0.1142 | 2.69000E+0 | 1 |
| 0.0644 | 4.76000E+1 | 1 | 0.1151 | 2.67000E+0 | 1 |
| 0.0655 | 4.55000E+1 | 1 | 0.1164 | 2.87000E+0 | 1 |
| 0.0657 | 3.37000E+1 | 1 | 0.1196 | 2.31000E+0 | 1 |
| 0.0663 | 4.15000E+1 | 1 | 0.1206 | 2.62000E+0 | 1 |
| 0.0663 | 4.03000E+1 | 1 | 0.1207 | 2.55000E+0 | 1 |
| 0.0685 | 3.39000E+1 | 1 | 0.1209 | 2.14000E+0 | 1 |
| 0.0686 | 3.63000E+1 | 1 | 0.1247 | 1.96000E+0 | 1 |
| 0.0688 | 3.39000E+1 | 1 | 0.1295 | 1.62000E+0 | 1 |
| 0.0690 | 3.27000E+1 | 1 | 0.1323 | 1.59000E+0 | 1 |
| 0.0690 | 3.39000E+1 | 1 | 0.1387 | 1.25000E+0 | 1 |
| 0.0698 | 3.11000E+1 | 1 | 0.1395 | 1.29000E+0 | 1 |
| 0.0704 | 2.91000E+1 | 1 | 0.1411 | 1.20000E+0 | 1 |
| 0.0704 | 2.92000E+1 | 1 | 0.1451 | 1.09000E+0 | 1 |
| 0.0704 | 2.85000E+1 | 1 | 0.1464 | 1.09000E+0 | 1 |
| 0.0745 | 2.09000E+1 | 1 | 0.1503 | 9.61000E-1 | 1 |
| 0.0782 | 1.66000E+1 | 1 | 0.1510 | 9.78000E-1 | 1 |
| 0.0782 | 1.62000E+1 | 1 | 0.1583 | 8.07000E-1 | 1 |
| 0.0820 | 1.26000E+1 | 1 | 0.1600 | 8.06000E-1 | 1 |
| 0.0843 | 1.11000E+1 | 1 | 0.1644 | 7.10000E-1 | 1 |
| 0.0873 | 9.75000E+0 | 1 | 0.1673 | 6.93000E-1 | 1 |
Table 10.3. (Continued)
T90 (K) |
µ-(m2/V.s) |
Key |
T90 |
µ-(m2/V.s) |
Key |
| 0.1718 | 6.14000E-1 | 1 | 0.2914 | 1.20000E-1 | 1 |
| 0.1730 | 6.19000E-1 | 1 | 0.2920 | 1.12000E-1 | 2 |
| 0.1776 | 5.48000E-1 | 1 | 0.2937 | 1.21000E-1 | 1 |
| 0.1796 | 5.44000E-1 | 1 | 0.2965 | 1.18000E-1 | 1 |
| 0.1821 | 5.08000E-1 | 1 | 0.2972 | 1.13000E-1 | 1 |
| 0.1860 | 4.92000E-1 | 1 | 0.2990 | 1.15000E-1 | 1 |
| 0.1861 | 4.75000E-1 | 1 | 0.3010 | 1.02000E-1 | 2 |
| 0.1919 | 4.30000E-1 | 1 | 0.3017 | 1.09000E-1 | 1 |
| 0.1920 | 4.44000E-1 | 1 | 0.3029 | 9.99000E-2 | 1 |
| 0.1957 | 4.04000E-1 | 1 | 0.3072 | 1.03000E-1 | 1 |
| 0.1976 | 4.04000E-1 | 1 | 0.3076 | 1.06000E-1 | 1 |
| 0.2022 | 3.76000E-1 | 1 | 0.3111 | 9.25000E-2 | 2 |
| 0.2036 | 3.57000E-1 | 1 | 0.3118 | 1.02000E-1 | 1 |
| 0.2078 | 3.34000E-1 | 1 | 0.3132 | 9.73000E-2 | 1 |
| 0.2096 | 3.36000E-1 | 1 | 0.3182 | 9.62000E-2 | 1 |
| 0.2152 | 3.09000E-1 | 1 | 0.3202 | 9.14000E-2 | 1 |
| 0.2161 | 2.97000E-1 | 1 |