Russell J. Donnelly
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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 2.176788956 7.73000E+01 7
2.176636230 6.37000E+01 7 2.176789967 7.76000E+01 7
2.176645370 6.40000E+01 7 2.176790000 7.77000E+01 6
2.176655790 6.46000E+01 7 2.176790000 7.76504E+01 5
2.176665910 6.46000E+01 7 2.176790200 7.80000E+01 6
2.176671800 6.52800E+01 6 2.176790792 7.77000E+01 7
2.176675720 6.53000E+01 7 2.176791479 7.87000E+01 7
2.176678000 6.55100E+01 6 2.176792234 7.88000E+01 7
2.176678500 6.53700E+01 6 2.176792744 7.87000E+01 7
2.176685000 6.57000E+01 7 2.176793259 8.02000E+01 7
2.176695450 6.59000E+01 7 2.176793869 8.05000E+01 7
2.176700000 6.60829E+01 5 2.176794309 8.04000E+01 7
2.176704242 6.65000E+01 7 2.176794761 8.10000E+01 7
2.176710628 6.70000E+01 7 2.176795229 8.13000E+01 7
2.176716977 6.73000E+01 7 2.176795659 8.16000E+01 7
2.176723343 6.78000E+01 7 2.176795979 8.21000E+01 7
2.176728740 6.76000E+01 7 2.176796282 8.23000E+01 7
2.176734305 6.85000E+01 7 2.176796663 8.29000E+01 7
2.176738974 6.92000E+01 7 2.176796931 8.42000E+01 7
2.176744134 6.90000E+01 7 2.176797220 8.38000E+01 7
2.176748459 6.95000E+01 7 2.176797379 8.41000E+01 7
2.176750000 6.96452E+01 5 2.176797628 8.47000E+01 7
2.176751982 7.02000E+01 7 2.176797839 8.56000E+01 7
2.176755459 7.03000E+01 7 2.176798079 8.56000E+01 7
2.176758801 7.06000E+01 7 2.176798200 8.58000E+01 7
2.176762052 7.12000E+01 7 2.176798379 8.64000E+01 7
2.176764908 7.15000E+01 7 2.176798527 8.79000E+01 7
2.176767701 7.18000E+01 7 2.176798835 8.88000E+01 7
2.176769257 7.13000E+01 7 2.176798931 8.86000E+01 7
2.176771289 7.26000E+01 7 2.176799028 8.87000E+01 7
2.176773790 7.27000E+01 7 2.176799128 8.93000E+01 7
2.176775441 7.34000E+01 7 2.176799229 8.99000E+01 7
2.176777369 7.36000E+01 7 2.176799328 9.05000E+01 7
2.176779885 7.44000E+01 7 2.176799429 9.14000E+01 7
2.176780000 7.38480E+01 5 2.176799523 9.26000E+01 7
2.176780922 7.47000E+01 7 2.176799584 9.24000E+01 7
2.176781000 7.40000E+01 6 2.176799650 9.28000E+01 7
2.176781600 7.59000E+01 6 2.176799725 9.47000E+01 7
2.176782511 7.51000E+01 7 2.176799768 9.59000E+01 7

Table 7.1. (Continued)


T90 (K)

Cs (J/mol·K)

Key

T90

u1 (m/s)

Key
2.176799822 9.65000E+01 7 2.176807642 5.95000E+01 7
2.176799860 9.72000E+01 7 2.176808443 5.92000E+01 7
2.176799909 1.00000E+02 7 2.176809033 5.85000E+01 7
2.176799965 1.04100E+02 7 2.176809600 5.68000E+01 6
2.176800132 7.95000E+01 7 2.176809698 5.81000E+01 7
2.176800144 7.97000E+01 7 2.176810000 5.76000E+01 6
2.176800164 7.99000E+01 7 2.176810000 5.76374E+01 5
2.176800185 7.95000E+01 7 2.176810569 5.78000E+01 7
2.176800220 7.89000E+01 7 2.176811400 5.71000E+01 6
2.176800269 7.67000E+01 7 2.176811505 5.71000E+01 7
2.176800293 7.60000E+01 7 2.176812520 5.69000E+01 7
2.176800320 7.68000E+01 7 2.176813463 5.63000E+01 7
2.176800371 7.56000E+01 7 2.176814493 5.64000E+01 7
2.176800400 7.36000E+01 7 2.176815612 5.58000E+01 7
2.176800420 7.33000E+01 7 2.176816537 5.52000E+01 7
2.176800494 7.35000E+01 7 2.176816800 5.37000E+0 6
2.176800593 7.24000E+01 7 2.176817900 5.46000E+01 6
2.176800692 7.15000E+01 7 2.176818091 5.48000E+01 7
2.176800797 7.07000E+01 7 2.176819577 5.45000E+01 7
2.176800896 7.04000E+01 7 2.176820000 5.46355E+01 5
2.176800998 6.99000E+01 7 2.176821081 5.42000E+01 7
2.176801097 6.95000E+01 7 2.176823067 5.35000E+01 7
2.176801171 6.88000E+01 7 2.176825087 5.35000E+01 7
2.176801296 6.83000E+01 7 2.176827095 5.30000E+01 7
2.176801363 6.84000E+01 7 2.176829050 5.26000E+01 7
2.176801494 6.76000E+01 7 2.176831035 5.25000E+01 7
2.176801568 6.79000E+01 7 2.176832778 5.18000E+01 7
2.176801724 6.81000E+01 7 2.176835750 5.12000E+01 7
2.176801849 6.62000E+01 7 2.176837100 5.10000E+01 6
2.176801969 6.64000E+01 7 2.176838888 5.06000E+01 7
2.176802149 6.66000E+01 7 2.176841885 5.05000E+01 7
2.176802342 6.58000E+01 7 2.176844784 5.00000E+01 7
2.176802516 6.52000E+01 7 2.176848510 4.98000E+01 7
2.176802675 6.44000E+01 7 2.176850000 4.96322E+01 5
2.176802906 6.40000E+01 7 2.176852300 4.93000E+01 6
2.176803147 6.37000E+01 7 2.176852561 4.92000E+01 7
2.176803331 6.35000E+01 7 2.176856247 4.90000E+01 7
2.176803593 6.31000E+01 7 2.176861043 4.88000E+01 7
2.176803900 6.28000E+01 7 2.176866602 4.78000E+01 7
2.176804196 6.25000E+01 7 2.176871084 4.77000E+01 7
2.176804544 6.18000E+01 7 2.176872600 4.73000E+01 6
2.176804944 6.14000E+01 7 2.176876677 4.74000E+01 7
2.176805319 6.13000E+01 7 2.176882637 4.68000E+01 7
2.176805743 6.08000E+01 7 2.176888300 4.64000E+01 6
2.176806207 6.02000E+01 7 2.176888888 4.68000E+01 7
2.176806697 6.00000E+01 7 2.176889500 4.61400E+01 6
2.176807203 5.95000E+01 7 .176897038 4.63000E+01 7

Table 7.1. (Continued)

3

T90 (K)

Cs (J/mol·K)

Key

T90

u1 (m/s)

Key
2.176900000 4.52694E+01 5 2.178240900 3.15000E+01 7
2.176905090 4.56000E+01 7 2.178341000 3.12000E+01 7
2.176915210 4.50000E+01 7 2.178390000 3.11803E+01 5
2.176924970 4.47000E+01 7 2.178450300 3.09000E+01 7
2.176934900 4.45000E+01 7 2.178524000 3.04300E+01 6
2.176945050 4.36000E+01 7 2.178590400 3.03000E+01 7
2.176955460 4.36000E+01 7 2.178678000 2.99900E+01 6
2.176964320 4.31000E+01 7 2.178740200 3.00000E+01 7
2.176972800 4.27500E+01 6 2.178827700 2.99000E+01 7
2.176979650 4.27000E+01 7 2.178869000 600E+01 6
2.176995040 4.19000E+01 7 2.179214000 2.86400E+01 6
2.177000000 4.23075E+01 5 2.179310000 2.87387E+01 5
2.177010690 4.19000E+01 7 2.179553000 2.79300E+01 6
2.177028050 4.14000E+01 7 2.179814000 2.74800E+01 6
2.177037900 4.10800E+01 6 2.179880000 2.73300E+01 6
2.177043600 4.11000E+01 7 2.180204000 2.68000E+01 6
2.177065760 4.06000E+01 7 2.180749000 2.60400E+01 6
2.177066000 4.04300E+01 6 2.180780000 2.65372E+01 5
2.177087900 4.04000E+01 7 2.181431000 2.52000E+01 6
2.177109540 3.99000E+01 7 2.181963955 2.44400E+01 6
2.177129670 3.95000E+01 7 2.182673184 2.37700E+01 6
2.177159490 3.90000E+01 7 2.182925239 2.36954E+01 5
2.177189620.85000E+01 7 2.186624998 2.12138E+01 5
2.177219030 3.84000E+01 7 2.192523901 1.87722E+01 5
2.177238300 3.77800E+01 6 2.201723640 1.65708E+01 5
2.177250520 3.80000E+01 7 2.203823802 1.59304E+01 8
2.177282540 3.71000E+01 7 2.216426239 1.46535E+01 5
2.177300000 3.68239E+01 5 2.23973624 1.28363E+01 5
2.177309700 3.69800E+01 6 2.25384544 1.21679E+01 8
2.177319440 3.70000E+01 7 2.276666284 1.14194E+01 5
2.177369760 3.65000E+01 7 2.304205527 1.05669E+01 8
2.177421430 3.60000E+01 7 2.354513418 9.88647E+00 8
2.177461300 3.58000E+01 7 2.404936229 9.52620E+00 8
2.177485500 3.54100E+01 6 2.505557267 9.12590E+00 8
2.177510100 3.53000E+01 7 2.606086904 9.08590E+00 8
2.177570830 3.48000E+01 7 2.706596360 9.16590E+00 8
2.177628930 3.45000E+01 7 2.807058930 9.36610E+00 8
2.177700280 3.40000E+01 7 2.907241720 9.64630E+00 8
2.177771260 3.37000E+01 7 3.007401739 9.96650E+00 8
2.177800000 3.34617E+01 5 .107543262 1.03267E+01 8
2.177825000 3.32200E+01 6 3.207478906 1.07670E+01 8
2.177850200 3.32000E+01 7 3.307424279 1.13274E+01 8
2.177938900 3.28000E+01 7 3.407351902 1.18877E+01 8
2.177984000 3.25000E+01 6 3.507252795 1.24481E+01 8
2.178029200 3.24000E+01 7 3.607129693 1.30485E+01 8
2.178129400 3.20000E+01 7 3.707066600 1.36889E+01 8
3.907137696 1.51299E+01 8 4.659780505 2.48960E+01 8
4.007233994 1.59704E+01 8 4.710078203 2.62970E+01 8
4.107360133 1.69311E+01 8 4.760314859 2.81780E+01 8
4.207682570 1.79317E+01 8 4.810536961 3.01400E+01 8
4.307978467 1.91320E+01 > 8 4.860791389 3.29010E+01 8
4.408382309 2.04530E+01 8 4.911025444 3.61430E+01 8
4.508963741 2.20140E+01 8 4.961186960 4.04260E+01 8
4.559218620 2.28950E+01 8 5.011324184 4.60300E+01 8
4.609475809 2.37750E+01 8 5.061435817 5.40350E+01 8

Table 7.2. Knots and coefficients for the spline fit of log10 Cs for T < T


Knots

Coefficients
K(1) = 1.00000000000E-2 C(1) = -7.080029E+0
K(2) = 1.00000000000E-2 C(2) = -6.461204E+0
K(3) = 1.00000000000E-2 C(3) = -5.407887E+0
K(4) = 1.00000000000E-2 C(4) = -4.971098E+0
K(5) = 2.49738990740E-2 C(5) = -4.092648E+0
K(6) = 6.07641105990E-2 C(6) = -3.430290E+0
K(7) = 6.36528653770E-2 C(7) = -2.300493E+0
K(8) = 1.54157179076E-1 C(8) = -1.865551E+0
K(9) = 2.49299135447E-1 C(9) = -6.120157E-1
K(10) = 6.34497077644E-1 C(10) = 1.800753E-1
K(11) = 9.04465380669E-1 C(11) = 8.200057E-1
K(12) = 1.17474564385E+0 C(12) = 1.231093E+0
K(13) = 1.54255910867E+0 C(13) = 1.494099E+0
K(14) = 2.06499088720E+0 C(14) = 1.633977E+0
K(15) = 2.16070930746E+0 C(15) = 1.694854E+0
K(16) = 2.17157525125E+0 C(16) = 1.760367E+0
K(17) = 2.17590629200E+0 C(17) = 1.813528E+0
K(18) = 2.17655315900E+0 C(18) = 1.849639E+0
K(19) = 2.17672849900E+0 C(19) = 1.900049E+0
K(20) = 2.17678788100E+0 C(20) = 1.935770E+0
K(21) = 2.17679663200E+0 C(21) = 1.974983E+0
K(22) = 2.17679958200E+0 C(22) = 2.017442E+0
K(23) = 2.17679996468E+0  
K(24) = 2.17679996468E+0  
K(25) = 2.17679996468E+0  
K(26) = 2.17679996468E+0  

.Table 7.3. Knots and coefficients for the spline fit of log10 Cs for T > T.


Knots

Coefficients
K(1) = 2.17680013200E+0 C(1) = 1.900539E+0
K(2) = 2.17680013200E+0 C(2) = 1.862865E+0
K(3) = 2.17680013200E+0 C(3) = 1.822431E+0
K(4) = 2.17680013200E+0 C(4) = 1.759056E+0
K(5) = 2.17680101200E+0 C(5) = 1.679157E+0
K(6) = 2.17680349500E+0 C(6) = 1.584631E+0
K(7) = 2.17681801800E+0 C(7) = 1.464344E+0
K(8) = 2.17692420600E+0 C(8) = 1.274043E+0
K(9) = 2.17750755600E+0 C(9) = 1.095050E+0
K(10) = 2.18086397100E+0 C(10) = 9.546039E-1
K(11) = 2.20374020794E+0 C(11) = 9.503531E-1
K(12) = 2.30368058865E+0 C(12) = 1.100724E+0
K(13) = 2.60849038128E+0 C(13) = 1.260996E+0
K(14) = 3.60335763894E+0 C(14) = 1.421360E+0
K(15) = 4.41358469422E+0 C(15) = 1.609738E+0
K(16) = 4.81404577042E+0 C(16) = 1.732672E+0
K(17) = 5.06143581698E+0  
K(18) = 5.06143581698E+0  
K(19) = 5.06143581698E+0  
K(20) = 5.06143581698E+0  


Table 7.4. Recommended values of the heat capacity of liquid 4He


T90 (K)

Cs (J/mol·K)

T90 (K)

Cs (J/mol·K)
0.0000 0 2.2000 1.673E+1
0.0500 1.023E-05 2.2500 1.228E+1
0.1000 8.250E-05 2.3000 1.078E+1
0.1500 2.824E-4 2.3500 1.001E+1
0.2000 6.597E-4 2.4000 9.515E+0
0.2500 1.267E-3 2.4500 9.225E+0
0.3000 2.172E-3 2.5000 9.083E+0
0.3500 3.431E-3 2.5500 9.043E+0
0.4000 5.086E-3 2.6000 9.066E+0
0.4500 7.206E-3 2.6500 9.117E+0
0.5000 9.939E-3 2.7000 9.186E+0
0.5500 1.359E-2 2.7500 9.271E+0
0.6000 1.877E-2 2.8000 9.374E+0
0.6500 2.665E-2 2.8500 9.493E+0
0.7000 3.919E-2 2.9000 9.628E+0
0.7500 5.901E-2 2.9500 9.778E+0
0.8000 8.976E-2 3.0000 9.944E+0
0.8500 1.361E-1 3.0500 1.012E+1
0.9000 2.030E-1 3.1000 1.032E+1
0.9500 2.946E-1 3.1500 1.053E+1
1.0000 4.154E-1 3.2000 1.075E+1
1.0500 5.707E-1 3.2500 1.099E+1
1.1000 7.658E-1 3.3000 1.124E+1
1.1500 1.006E+0 3.3500 1.151E+1
1.2000 1.297E+0 3.4000 1.178E+1
1.2500 1.646E+0 3.4500 1.207E+1
1.3000 2.057E+0 3.5000 1.237E+1
1.3500 2.537E+0 3.5500 1.268E+1
1.4000 3.092E+0 3.6000 1.300E+1
1.4500 3.732E+0 3.6500 1.333E+1
1.5000 4.468E+0 3.7000 1.366E+1
1.5500 5.313E+0 3.7500 1.401E+1
1.6000 6.285E+0 3.8000 1.437E+1
1.6500 7.401E+0 3.8500 1.475E+1
1.7000 8.678E+0 3.9000 1.513E+1
1.7500 1.014E+1 3.9500 1.554E+1
1.8000 1.181E+1 4.0000 1.596E+1
1.8500 1.372E+1 4.0500 1.640E+1
1.9000 1.590E+1 4.1000 1.687E+1
1.9500 1.841E+1 4.1500 1.736E+1
2.0000 2.128E+1 4.2000 1.788E+1
2.0500 2.459E+1 4.2500 1.84E+01
2.1000 2.864E+1 4.3000 1.90E+01
2.1500 3.689E+1 4.3500 1.96E+01
2.1760 5.569E+1 4.4000 2.03E+01
2.1761 5.623E+1 4.4500 2.10E+01
2.1762 5.692E+1 4.5000 2.18E+01
2.1763 5.784E+1 4.5500 2.26E+01
2.1764 5.906E+1 4.6000 2.36E+01
2.1765 6.068E+1 4.6500 2.48E+01
2.1766 6.283E+1 4.7000 2.61E+01
2.1767 6.640E+1 4.7500 2.78E+01
2.1768 - 4.8000 2.98E+01
2.1769 4.569E+1 4.8500 3.22E+01
2.1770 4.227E+1 4.9000 3.53E+01
2.1775 3.543E+1 4.9500 3.93E+01
2.1780 3.264E+1 5.0000 4.47E+01

Table 7.5. Knots and coefficients for the spline fit to the enthalpy of liquid 4He.


Knots

Coefficients
K(1)=0.000000 C(1)=0.000000E+00
K(2)=0.000000 C(2)=0.000000E+00
K(3)=0.000000 C(3)=-1.650000E-06
K(4)=0.000000 C(4)=1.801000E-05
K(5)=0.100000 C(5)=1.185000E-04
K(6)=0.200000 C(6)=4.108550E-04
K(7)=0.300000 C(7)=1.033200E-03
K(8)=0.370000 C(8)=2.710000E-03
K(9)=0.500000 C(9)=6.090000E-03
K(10)=0.610000 C(10)=1.784000E-02
K(11)=0.743950 C(11)=6.032740E-02
K(12)=0.870000 C(12)=2.400500E-01
K(13)=1.027550 C(13)=8.643720E-01
K(14)=1.250000 C(14)=2.445400E+00
K(15)=1.500000 C(15)=5.554360E+00
K(16)=1.750000 C(16)=8.800000E+00
K(17)=2.000000 C(17)=1.220130E+01
K(18)=2.130000 C(18)=1.558100E+01
K(19)=2.190120 C(19)=2.004000E+01
K(20)=2.232940 C(20)=3.223100E+01
K(21)=2.854200 C(21)=4.704640E+01
K(22)=4.000000 C(22)=5.848930E+01
K(23)=4.900000  
K(24)=4.900000  
K(25)=4.900000  
K(26)=4.900000  

Table 7.6. Recommended values of the enthalpy of liquid 4He.


T90 (K)

H (J mol-1)

T90 (K)

H (J mol-1)
0.10 2.039E-06 2.60 16.876
0.15 1.056E-05 2.65 17.332
0.20 3.334E-05 2.70 17.784
0.25 8.018E-05 2.75 18.237
0.30 1.651E-04 2.80 18.696
0.35 3.035E-04 2.85 19.168
0.40 5.130E-04 2.90 19.656
0.45 8.178E-04 2.95 20.162
0.50 1.250E-03 3.00 20.686
0.55 1.840E-03 3.05 21.228
0.60 2.640E-03 3.10 21.789
0.65 3.740E-03 3.15 22.367
0.70 5.370E-03 3.20 22.964
0.75 7.830E-03 3.25 23.580
0.80 1.152E-02 3.30 24.213
0.85 1.713E-02 3.35 24.866
0.90 2.543E-02 3.40 25.537
0.95 3.765E-02 3.45 26.227
1.00 5.535E-02 3.50 26.935
1.05 8.014E-02 3.55 27.662
1.10 1.140E-01 3.60 28.409
1.15 1.591E-01 3.65 29.174
1.20 2.180E-01 3.70 29.958
1.25 2.928E-01 3.75 30.762
1.30 3.863E-01 3.80 31.584
1.35 5.020E-01 3.85 32.426
1.40 6.436E-01 3.90 33.288
1.45 8.150E-01 3.95 34.168
1.50 1.020 4.00 35.069
1.55 1.263 4.05 35.989
1.60 1.553 4.10 36.933
1.65 1.899 4.15 37.905
1.70 2.311 4.20 38.908
1.75 2.799 4.25 39.946
1.80 3.370 4.30 41.024
1.85 4.028 4.35 42.146
1.90 4.775 4.40 43.315
1.95 5.615 4.45 44.535
2.00 6.548 4.50 45.811
2.05 7.607 4.55 47.146
2.10 8.945 4.60 48.545
2.15 10.724 4.65 50.011
2.20 12.340 4.70 51.548
2.25 13.104 4.75 53.160
2.30 13.743 4.80 54.852
2.35 14.340 4.85 56.627
2.40 14.899 4.90 58.489
2.45 15.427 4.95 60.443
2.50 15.929 5.00 62.491
2.55 16.410    

 

Chronological Bibliography for Heat Capacity and Enthalpy


1

H. C. Kramers, J. D. Wasscher, and C. J. Gorter, "The Specific Heat of Liquid Helium Between 0.25 and 1.9 Degrees K," Physica 18, 329-337 (1952).
2 G. R. Hercus and J. Wilks, “The Specific Heat of Liquid Helium II as a Function of Pressure,” Philos. Mag. 45, 1163-1172 (1954).
3 R. W. Hill and O. V. Lounasmaa, “The Specific Heat of Liquid Helium,” Philos. Mag. 2, 143-148 (1957).
4 W. M. Fairbank, M. J. Buckingham, and C. F. Keller, “Specific Heat of Liquid 4He Near the Lambda Point,” in 5th International Conference on Low Temperature Physics and Chemistry, edited by J. R. Dillinger (1958), pp. 50-52.
5 O. V. Lounasmaa and E. Kojo, “The Specific Heat Cv of Liquid Helium Near the Lambda Curve at Various Densities,” Ann. Acad. Scien. Fennicae A VI, Physica 36, 1 (1959).
6 M. J. Buckingham and W. M. Fairbank, “The Nature of the Lambda Transition in Liquid Helium,” in Progress in Low Temperature Physics, edited by C. G. Gorter (North Holland Publishing, 1961), Vol. 3, pp. 80-112.
7 C. J. N. Van den Meijdenberg, K. W. Taconis, and R. De Bruyn Ouboter, “The Entropy of Helium II Under Pressure from Measurements on the Fountain Effect,” Physica 27, 197-218 (1961).
8 W. M. Fairbank, “The Nature of the Lambda Transition in Liquid Helium,” in International School of Physics, Course XXI, edited by G. Careri (New York: Academic Press, 1963).
9 J. Wiebes, “Caloric Measurements on Liquid and Melting Helium Below 1.5 Kelvin,” Ph.D. Thesis, Kammerlingh Onnes Laboratory, 1969 (unpublished).
10 N. E. Phillips, C. G. Waterfield, and J. K. Hoffer, “Calorimetric Evidence for Positive Phonon Dispersion in Liquid 4He,” Phys. Rev. Lett. 25, 1260 (1970).
11 G. Ahlers, “Heat Capacity Near the Superfluid Transition in 4He at the Saturated Vapor Pressure,” Phys. Rev. A 3, 696-716 (1971).
12 S. A. Scott, E. Guyon, and I. Rudnick, “Specific Heat and Superfluid Density of Liquid Helium in Porous Media,” J. Low. Temp. Phys. 9, 389-407 (1972).
13 G. Ahlers, “Thermodynamics and Experimental Tests of Static Scaling and Universality Near the Superfluid Transition in 4He Under Pressure,” Phys. Rev. A 8, 530-568 (1973).
14 R. J. Donnelly and P. H. Roberts, “A Theory of Temperature-Dependent Energy Levels: Thermodynamic Properties of Helium II,” J. Low Temp. Phys. 27, 687-736 (1977).
15 D. S. Greywall, “Specific Heat and Phonon Dispersion Curve of Liquid 4He,” Phys. Rev. B 18, 2127-214 (1978).
16 D. S. Greywall, “Erratum: Specific Heat and Phonon Dispersion Curve of Liquid 4He,” Phys. Rev. B 21, 1329-1331 (1979).
17 J. A. Lipa and T. C. P. Chui, “Very High Resolution Heat-Capacity Measurements Near the Lambda Point of Helium,” Phys. Rev. Lett. 51, 2291-2294 (1983).
18 J. A. Lipa, D. R. Swanson, J. A. Nissen, T. C. P. Chui, and U. E. Israelsson, “Heat Capacity and Thermal Relaxation of Bulk Helium Very Near the Lambda Point,” Phys. Rev. Letters 76, 944 (1996).

 

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