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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 C_s is the heat capacity at saturation pressure.
10) Lipa et. al. Ref. 16 have measured C_s 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)

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 C_s 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 C_s 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

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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).
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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).
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