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 7. Heat Capacity and Enthalpy
Adopted Database
Author(s) |
Key # |
Method |
Range (K) |
Uncertainty % |
| Donnelly | 1 | Theory | 0.01
 T
0.06 |
NA |
| Greywall | 2 | Calorimeter | 0.0606
T
1.024 |
1 |
| Wiebes | 3 | Calorimeter | 0.3
T
1.6 |
2 |
| Phillips | 4 | Calorimeter | 0.32161
T
2.17805 |
1 |
| Buckingham | 5 | Calorimeter | 2.072
T
2.272 |
3 |
| Ahlers | 6 | Calorimeter | 2.17282
T
2.17805 |
1 |
| Lipa | 7 | Calorimeter | 2.1699103
T
2.1740277 |
1.5 |
| Hill | 8 | Calorimeter | 2.1992
T 5.50543
|
1 |
Comments and Key to Authors
1)
Ref. 14. Calculated from the Landau theory.
2) Ref. 15 and 16. Temperatures taken on 1962 3He Scale.
3) Ref. 9.
4) Ref. 10.
5) Ref. 6, page 85.
6) Ref. 11.
7) Ref. 17. Temperatures taken on the EPT-76 scale.
8) Ref. 3. Corrected to T58.
9) The spline is actually fit to , where Cs is the heat capacity
at saturation pressure.
10) Lipa et. al. Ref. 16 have measured Cs very near the lambda
point in a microgravity experiment. They fit their data using functions
of the type 
, where t=|
1+ T/T
|. was set at 0.5 above and below T.
The results were as follows:
|
|
A |
B |
D |
E |
| T<T |
-0.012850 | 5.7015 | 456.28 | -0.0228 | 0.323 |
| T>T |
-0.012850 | 6.0092 | 456.28 | -0.0228 | 0.323 |
The range of data for T
T
was , and for T
T
was . The data above T
are not considered as accurate as the data below T.
11) The enthalpy H of liquid helium can be deduced from the heat capacity
using the relation
where the second term arises because we are following along the saturated vapor pressure line. H is the difference between the total enthalpy and the ground state enthalpy (see J. S. Brooks and R. J. Donnelly, J. Phys. Chem. Ref. Data p. 51 1977, Section 4.3.d).
Figure
7.1. The recommended values for the heat capacity of liquid 4He as a function
of temperature at saturated vapor pressure.
12) We list recommended values of enthalpy directly from the above integration,
so the uncertainties reflect uncertainties in heat capacity. We have also
given a spline of the enthalpy for convenience of the reader. The spline
does not return the exact recommended values (see Fig. 7.7).
13) Most heat capacity measurements are reported in Joules/mol•K.
To convert data from J/g•K to J/mol•K multiply by 4.0026.
To convert from Joules/mol•K to J/kg•K multiply by 249.837.
The same factor is used to convert the units for enthalpy.
Figure
7.2. The recommended values for the heat capacity of liquid 4He at saturated
vapor pressure near expressed as vs Log10|T-T|.
Figure 7.3. The fractional deviation of values of the adopted database from the recommended values for the heat capacity of liquid 4He expressed in percent.
Figure
7.4. The fractional deviation of values of the adopted database from the
recommended values for the heat capacity of liquid 4He near the lambda
transition for T < T.
Figure
7.5. The fractional deviation of values of the adopted database from the
recommended values for the heat capacity of liquid 4He near the lambda
transition for T > T.
Figure 7.6. Values for the enthalpy of liquid 4He at saturated vapor pressure, obtained by integration of the recommended values of the heat capacity.
Figure 7.7. Fractional deviation of the spline fit of the recommended values of the enthalpy from the enthalpy integrated from recommended values of the heat capacity.
Table 7.1. Adopted database for heat capacity of liquid 4He at saturated vapor
T90 (K) |
Cs (J/mol·K) |
Key |
T90 |
u1 (m/s) |
Key |
| 0.010000000 | 8.31700E-08 | 1 | 0.332900000 | 2.95200E-03 | 2 |
| 0.015000000 | 2.80670E-07 | 1 | 0.337236048 | 3.05200E-03 | 4 |
| 0.020075015 | 6.65200E-07 | 1 | 0.339201980 | 3.16100E-03 | 4 |
| 0.025093607 | 1.29900E-06 | 1 | 0.349400000 | 3.39700E-03 | 2 |
| 0.030112134 | 2.24456E-06 | 1 | 0.351177931 | 3.48226E-03 | 3 |
| 0.035130597 | 3.56360E-06 | 1 | 0.353755696 | 3.58300E-03 | 4 |
| 0.040148997 | 5.31800E-06 | 1 | 0.358810557 | 3.73000E-03 | 4 |
| 0.045167333 | 7.57050E-06 | 1 | 0.366700000 | 3.90200E-03 | 2 |
| 0.050185606 | 1.03800E-05 | 1 | 0.371879445 | 4.13900E-03 | 4 |
| 0.055203817 | 1.38140E-05 | 1 | 0.380223962 | 4.40300E-03 | 4 |
| 0.060221963 | 1.79290E-05 | 1 | 0.384700000 | 4.48700E-03 | 2 |
| 0.060610000 | 1.70500E-05 | 2 | 0.391476993 | 4.79500E-03 | 4 |
| 0.063540000 | 1.97600E-05 | 2 | 0.401325554 | 5.24341E-03 | 3 |
| 0.066640000 | 2.31700E-05 | 2 | 0.401800000 | 5.09000E-03 | 2 |
| 0.069870000 | 2.71300E-05 | 2 | 0.403451755 | 5.25600E-03 | 4 |
| 0.073270000 | 3.16800E-05 | 2 | 0.412929109 | 5.59100E-03 | 4 |
| 0.076860000 | 3.67400E-05 | 2 | 0.417900000 | 5.71000E-03 | 2 |
| 0.080670000 | 4.28200E-05 | 2 | 0.428112594 | 6.23700E-03 | 4 |
| 0.084630000 | 4.96100E-05 | 2 | 0.433600000 | 6.36400E-03 | 2 |
| 0.088820000 | 5.73600E-05 | 2 | 0.436847534 | 6.59600E-03 | 4 |
| 0.093220000 | 6.66700E-05 | 2 | 0.448800000 | 7.03900E-03 | 2 |
| 0.097810000 | 7.70700E-05 | 2 | 0.451468481 | 7.44484E-03 | 3 |
| 0.102800000 | 8.99000E-05 | 2 | 0.454136258 | 7.44200E-03 | 4 |
| 0.108000000 | 1.04600E-04 | 2 | 0.463700000 | 7.75900E-03 | 2 |
| 0.113500000 | 1.21200E-04 | 2 | 0.464605602 | 7.94600E-03 | 4 |
| 0.119400000 | 1.41500E-04 | 2 | 0.478200000 | 8.51600E-03 | 2 |
| 0.125500000 | 1.64800E-04 | 2 | 0.483407690 | 8.97200E-03 | 4 |
| 0.132000000 | 1.91000E-04 | 2 | 0.492800000 | 9.34200E-03 | 2 |
| 0.138800000 | 2.22500E-04 | 2 | 0.497085329 | 9.78200E-03 | 4 |
| 0.146200000 | 2.60500E-04 | 2 | 0.501607656 | 1.02867E-02 | 3 |
| 0.153900000 | 3.02900E-04 | 2 | 0.507100000 | 1.02100E-02 | 2 |
| 0.161900000 | 3.52700E-04 | 2 | 0.514462524 | 1.08900E-02 | 4 |
| 0.170200000 | 4.09200E-04 | 2 | 0.521500000 | 1.11700E-02 | 2 |
| 0.179200000 | 4.77200E-04 | 2 | 0.523617428 | 1.15100E-02 | 4 |
| 0.188800000 | 5.56700E-04 | 2 | 0.535900000 | 1.22200E-02 | 2 |
| 0.198800000 | 6.49000E-04 | 2 | 0.546077483 | 1.32000E-02 | 4 |
| 0.209500000 | 7.56800E-04 | 2 | 0.550700000 | 1.34205E-02 | 2 |
| 0.220600000 | 8.82600E-04 | 2 | 0.551742562 | 1.40491E-02 | 3 |
| 0.231700000 | 1.01900E-03 | 2 | 0.555683078 | 1.40300E-02 | 4 |
| 0.244100000 | 1.18900E-03 | 2 | 0.565687962 | 1.47675E-02 | 2 |
| 0.257300000 | 1.38900E-03 | 2 | 0.576517791 | 1.60300E-02 | 4 |
| 0.272200000 | 1.64100E-03 | 2 | 0.580874318 | 1.62819E-02 | 2 |
| 0.286700000 | 1.90900E-03 | 2 | 0.588478962 | 1.73300E-02 | 4 |
| 0.301025619 | 2.20143E-03 | 3 | 0.596225336 | 1.80215E-02 | 2 |
| 0.301900000 | 2.22300E-03 | 2 | 0.601873568 | 1.94927E-02 | 3 |
| 0.317100000 | 2.57000E-03 | 2 | 0.612103323 | 2.00869E-02 | 2 |
| 0.322702023 | 2.69800E-03 | 4 | 0.612310364 | 2.04600E-02 | 4 |
Table 7.1. (Continued)
T90 (K) |
Cs (J/mol·K) |
Key |
T90 |
u1 (m/s) |
Key |
| 0.626807284 | 2.26300E-02 | 4 | 1.388218288 | 3.01900E+00 | 4 |
| 0.628517095 | 2.25628E-02 | 2 | 1.403515049 | 3.09001E+00 | 3 |
| 0.645456333 | 2.55163E-02 | 2 | 1.453556614 | 3.72642E+00 | 3 |
| 0.648852852 | 2.65700E-02 | 4 | 1.503597910 | 4.46290E+00 | 3 |
| 0.651991318 | 2.78981E-02 | 3 | 1.505409334 | 4.58000E+00 | 4 |
| 0.662934853 | 2.90934E-02 | 2 | 1.505899719 | 4.68500E+00 | 4 |
| 0.681197115 | 3.34762E-02 | 2 | 1.553637123 | 5.32346E+00 | 3 |
| 0.691277949 | 3.70400E-02 | 4 | 1.582153782 | 5.90600E+00 | 4 |
| 0.700368882 | 3.90665E-02 | 2 | 1.603690373 | 6.31610E+00 | 3 |
| 0.702124626 | 4.11868E-02 | 3 | 1.635233195 | 7.20800E+00 | 4 |
| 0.708499999 | 4.25700E-02 | 4 | 1.658829565 | 7.56400E+00 | 4 |
| 0.720452604 | 4.59791E-02 | 2 | 1.754802154 | 1.02300E+01 | 4 |
| 0.741502751 | 5.47328E-02 | 2 | 1.776611822 | 1.10800E+01 | 4 |
| 0.750478191 | 6.05000E-02 | 4 | 1.865627080 | 1.43200E+01 | 4 |
| 0.752244790 | 6.18402E-02 | 3 | 1.916469079 | 1.65500E+01 | 4 |
| 0.763992981 | 6.60381E-02 | 2 | 1.992102080 | 2.08800E+01 | 4 |
| 0.766438104 | 6.88300E-02 | 4 | 1.996426104 | 2.07500E+01 | 4 |
| 0.787875344 | 8.05773E-02 | 2 | 2.052220307 | 2.47400E+01 | 4 |
| 0.802361834 | 9.28603E-02 | 3 | 2.062756913 | 2.56400E+01 | 4 |
| 0.814481920 | 1.00959E-01 | 2 | 2.063718535 | 2.56800E+01 | 4 |
| 0.815742366 | 1.03700E-01 | 4 | 2.065000728 | 2.58100E+01 | 4 |
| 0.836419447 | 1.23600E-01 | 4 | 2.066713713 | 2.59400E+01 | 4 |
| 0.841734070 | 1.26561E-01 | 2 | 2.068767375 | 2.61400E+01 | 4 |
| 0.852475684 | 1.38890E-01 | 3 | 2.070811114 | 2.63000E+01 | 4 |
| 0.871304640 | 1.60808E-01 | 2 | 2.076331708 | 2.63771E+01 | 5 |
| 0.877089828 | 1.68900E-01 | 4 | 2.113325831 | 3.06599E+01 | 5 |
| 0.902586267 | 2.05734E-01 | 3 | 2.123709861 | 3.26700E+01 | 4 |
| 0.903629130 | 2.07131E-01 | 2 | 2.136704232 | 3.36619E+01 | 5 |
| 0.906374498 | 2.11000E-01 | 4 | 2.140798148 | 3.40400E+01 | 6 |
| 0.939237630 | 2.70084E-01 | 2 | 2.144510586 | 3.49400E+01 | 6 |
| 0.943765008 | 2.78600E-01 | 4 | 2.148814681 | 3.58900E+01 | 6 |
| 0.952694176 | 2.98594E-01 | 3 | 2.151453098 | 3.68239E+01 | 5 |
| 0.975031504 | 3.47300E-01 | 4 | 2.159768125 | 3.91700E+01 | 6 |
| 0.978888050 | 3.57773E-01 | 2 | 2.160680705 | 3.95857E+01 | 5 |
| 1.002776612 | 4.23075E-01 | 3 | 2.160690733 | 3.94800E+01 | 6 |
| 1.012518339 | 4.46700E-01 | 4 | 2.162395451 | 3.97600E+01 | 6 |
| 1.023530400 | 4.81150E-01 | 2 | 2.165754329 | 4.17600E+01 | 6 |
| 1.052861275 | 5.83579E-01 | 3 | 2.166596462 | 4.23000E+01 | 6 |
| 1.088881255 | 7.17000E-01 | 4 | 2.166596462 | 4.22274E+01 | 5 |
| 1.102955222 | 7.84109E-01 | 3 | 2.167318259 | 4.30600E+01 | 4 |
| 1.153029266 | 1.02867E+00 | 3 | 2.167439558 | 4.27600E+01 | 6 |
| 1.172802215 | 1.14300E+00 | 4 | 2.168030001 | 4.33000E+01 | 4 |
| 1.203266846 | 1.32086E+00 | 3 | 2.168932168 | 4.40900E+01 | 4 |
| 1.253202675 | 1.66508E+00 | 3 | 2.169107584 | 4.38900E+01 | 6 |
| 1.277869986 | 1.91000E+00 | 4 | 2.169543609 | 4.45600E+01 | 4 |
| 1.303323993 | 2.06934E+00 | 3 | 2.169944542 | 4.46000E+01 | 6 |
| 1.353442881 | 2.54165E+00 | 3 | 2.170072838 | 4.46700E+01 | 6 |
Table 7.1. (Continued)
T90 (K) |
Cs (J/mol·K) |
Key |
T90 |
u1 (m/s) |
Key |
| 2.170305372 | 4.48691E+01 | 5 | 2.175579900 | 5.35000E+01 | 7 |
| 2.170405602 | 4.55200E+01 | 4 | 2.175647000 | 5.40200E+01 | 6 |
| 2.170406604 | 4.49200E+01 | 6 | 2.175670300 | 5.40000E+01 | 7 |
| 2.170744372 | 4.52500E+01 | 6 | 2.175717000 | 5.42800E+01 | 6 |
| 2.170936807 | 4.61800E+01 | 4 | 2.175745000 | 5.44400E+01 | 6 |
| 2.171087144 | 4.55400E+01 | 6 | 2.175760500 | 5.43000E+01 | 7 |
| 2.171287593 | 4.58100E+01 | 4 | 2.175792000 | 5.46000E+01 | 6 |
| 2.171438929 | 4.59300E+01 | 6 | 2.175800000 | 5.45554E+01 | 5 |
| 2.171528127 | 4.67700E+01 | 4 | 2.175831310 | 5.48000E+01 | 7 |
| 2.171973000 | 4.62700E+01 | 6 | 2.175899950 | 5.52000E+01 | 7 |
| 2.172030000 | 4.70500E+01 | 4 | 2.175911900 | 5.52200E+01 | 6 |
| 2.172151000 | 4.65200E+01 | 6 | 2.175960800 | 5.55600E+01 | 6 |
| 2.172320000 | 4.82000E+01 | 4 | 2.175970830 | 5.56000E+01 | 7 |
| 2.172428000 | 4.68600E+01 | 6 | 2.176002800 | 5.59200E+01 | 6 |
| 2.172645000 | 4.70700E+01 | 6 | 2.176029750 | 5.59000E+01 | 7 |
| 2.172820000 | 4.71106E+01 | 5 | 2.176050500 | 5.62000E+01 | 6 |
| 2.172830000 | 4.82900E+01 | 4 | 2.176080300 | 5.63600E+01 | 6 |
| 2.172983000 | 4.76000E+01 | 6 | 2.176090610 | 5.62000E+01 | 7 |
| 2.173111000 | 4.77900E+01 | 6 | 2.176129200 | 5.67200E+01 | 6 |
| 2.173322000 | 4.80600E+01 | 6 | 2.176141490 | 5.67000E+01 | 7 |
| 2.173664000 | 4.86100E+01 | 6 | 2.176175600 | 5.70300E+01 | 6 |
| 2.173710000 | 4.97300E+01 | 4 | 2.176180490 | 5.69000E+01 | 7 |
| 2.173767000 | 4.88600E+01 | 6 | 2.176230510 | 5.76000E+01 | 7 |
| 2.174008000 | 4.92300E+01 | 6 | 2.176281960 | 5.79000E+01 | 7 |
| 2.174173000 | 4.96100E+01 | 6 | 2.176282500 | 5.79700E+01 | 6 |
| 2.174290000 | 4.97123E+01 | 5 | 2.176297000 | 5.83000E+01 | 6 |
| 2.174340000 | 4.98800E+01 | 6 | 2.176300000 | 5.75974E+01 | 5 |
| 2.174673000 | 5.06500E+01 | 6 | 2.176302700 | 5.83200E+01 | 6 |
| 2.174710300 | 5.06000E+01 | 7 | 2.176313500 | 5.83400E+01 | 6 |
| 2.174843000 | 5.11200E+01 | 6 | 2.176319470 | 5.83000E+01 | 7 |
| 2.174860600 | 5.12000E+01 | 7 | 2.176326100 | 5.84600E+01 | 6 |
| 2.175044000 | 5.17100E+01 | 6 | 2.176351800 | 5.89800E+01 | 6 |
| 2.175075000 | 5.17900E+01 | 6 | 2.176380650 | 5.91000E+01 | 7 |
| 2.175079000 | 5.18400E+01 | 6 | 2.176410970 | 5.95000E+01 | 7 |
| 2.175140500 | 5.21000E+01 | 7 | 2.176441060 | 5.99000E+01 | 7 |
| 2.175210000 | 5.23540E+01 | 5 | 2.176446700 | 6.00400E+01 | 6 |
| 2.175244000 | 5.22800E+01 | 6 | 2.176465200 | 6.03100E+01 | 6 |
| 2.175261600 | 5.24000E+01 | 7 | 2.176471930 | 6.02000E+01 | 7 |
| 2.175318000 | 5.26000E+01 | 6 | 2.176482200 | 6.05000E+01 | 6 |
| 2.175370300 | 5.26000E+01 | 7 | 2.176489950 | 6.04000E+01 | 7 |
| 2.175383000 | 5.28500E+01 | 6 | 2.176511500 | 6.10500E+01 | 6 |
| 2.175411000 | 5.29300E+01 | 6 | 2.176517430 | 6.11000E+01 | 7 |
| 2.175480300 | 5.31000E+01 | 7 | 2.176537170 | 6.14000E+01 | 7 |
| 2.175514000 | 5.33200E+01 | 6 | 2.176556820 | 6.18000E+01 | 7 |
| 2.175578000 | 5.35800E+01 | 6 | 2.176572560 | 6.20000E+01 | 7 |
T90 (K) |
Cs (J/mol·K) |
Key |
T90 |
u1 (m/s) |
Key |
| 2.176583200 | 6.24000E+01 | 6 | 2.176783965 | 7.57000E+01 | 7 |
| 2.176589940 | 6.27000E+01 | 7 | 2.176784972 | 7.60000E+01 | 7 |
| 2.176600000 | 6.12398E+01 | 5 | 2.176785500 | 7.60000E+01 | 6 |
| 2.176606060 | 6.32000E+01 | 7 | 2.176785700 | 7.71000E+01 | 6 |
| 2.176615000 | 6.32900E+01 | 6 | 2.176786010 | 7.61000E+01 | 7 |
| 2.176619900 | 6.37000E+01 | 6 | 2.176787021 | 7.65000E+01 | 7 |
| 2.176620470 | 6.32000E+01 | 7 | 2.176787994 | 7.69000E+01 | 7 |
| 2.176631500 | 6.38800E+01 | 6 |