PVT Measurements, Virial Coefficients, and Joule-Thomson inversion Curve of Fluorine

Abstract

Experimental PVT measurements on gaseous and liquid fluorine from the triple point (53.5 K) to 300 K at pressures to about 21 MN/m² are presented. The data are represented by a truncated virial equation in the low-density region. Comparisons of the second virial coefficient from this equation are made with published data. The PVT relationship along the Joule-Thomson inversion curve was obtained from the isotherm-isochore representation of the high density region.

1. Introduction

This laboratory is currently engaged in a comprehensive program to determine the thermodynamic and transport properties of compressed liquid and gaseous fluorine. Extensive, precise, PVT data are essential to the calculation of thermodynamic functions required for engineering development of proposed rocket propulsion systems. Since fluorine is not only the most reactive of all elements but also extremely toxic, it is not surprising that physical properties data on this fluid have either been inconsistent or, in many cases, nonexistent. Recently, however, some thermodynamic data have been reported by the authors of this paper [1, 2, 3].¹ The equations representing these data are given in the appendix of this paper for the sake of completeness.

It is the purpose of this paper to report new experimental PVT data from the triple point (53.5 K) to 300 K for pressures to a maximum of 21 MN/m² (1 MN/m² = 9.86923 atm). Also reported are derived values for the second and third virial coefficients and the Joule-Thomson inversion curve.

2. PVT Measurements

The experimental apparatus and instrumentation used for the PVT measurements on fluorine have been described earlier [4]. To measure single-phase densities, the common gas expansion method was used. After filling and closing off the sample holder, a sequence of pressure-temperature observations were made on the nearly constant density fluid confined in the PVT cell whose volume was accurately calibrated. Temperatures were regulated at integral values (on IPTS 1948 and the NBS 1955 temperature scale) to permit analysis of the data along isotherms. The temperatures of table 1, however, were converted to IPTS 1968 using the temperature scale differences given by references [5, 6]. When either maximum pressure (21 MN/m²) cr maximum temperature (300 K) was reached, the fluorine sample in the PVT cell was expanded into large calibrated volumes maintained near room temperature. The density could then be determined since the volume of the sample holder and the compressibility factor, PV/RT, of fluorine gas at the conditions in the expansion volumes were known. This fluorine compressibility factor was obtained using Burnett [7] gas expansion techniques. The results of all volume calibrations necessary for the density determination and the Burnett expansion experiment may be obtained from reference [8].

Table 1.

TEMPERATURE-PRESSURE-DENSITY OBSERVATIONS ON FLUORINE

TEMP K	PRESSURE MN/M2	DENSITY MOL/L	IDENT
74.994	0.0231	0.0379	13101
79.991	0.0249	0.0378	13102
84.997	0.0265	0.0378	13103
90.010	0.0280	0.0378	13104
95.013	0.0296	0.0378	13105
100.010	0.0312	0.0378	13106
109.998	0.0343	0.0377	13107
119.989	0.0374	0.0377	13108
129.987	0.0405	0.0377	13109
139.992	0.0436	0.0376	13110
79.991	0.0479	0.0740	13001
84.997	0.0513	0.0739	13002
90.010	0.0544	0.0739	13003
95.013	0.0575	0.0738	13004
100.010	0.0606	0.0738	13005
109.998	0.0667	0.0737	13006
119.989	0.0729	0.0737	13007
129.987	0.0789	0.0776	13008
139.992	0.0850	0.0735	13009
84.997	0.0955	0.1403	12901
90.010	0.1020	0.1403	12902
95.013	0.1080	0.1402	12903
100.010	0.1139	0.1401	12904
105.004	0.1198	0.1401	12905
119.989	0.1373	0.1398	12906
129.987	0.1489	0.1397	12907
139.992	0.1605	0.1396	12908
90.010	0.1516	0.2118	12801
95.013	0.1609	0.2117	12802
100.010	0.1699	0.2116	12803
105.004	0.1789	0.2115	12804
109.998	0.1879	0.2114	12805
119.989	0.2057	0.2111	12806
129.987	0.2234	0.2109	12807
139.992	0.2410	0.2107	12808
95.013	0.2640	0.3576	12301
100.010	0.2803	0.3574	12302
109.998	0.3112	0.3571	12303
119.989	0.3417	0.3567	12304
129.987	0.3721	0.3563	12305
139.992	0.4022	0.3559	12306
102.008	0.4305	0.5538	12701
105.004	0.4454	0.5537	12702
109.998	0.4699	0.5534	12703
114.994	0.4942	0.5531	12704
119.989	0.5183	0.5528	12705
129.987	0.5661	0.5522	12706
139.992	0.6136	0.5516	12707
105.004	0.6031	0.7767	12501
109.998	0.6390	0.7763	12502
114.994	0.6740	0.7759	12503
119.989	0.7086	0.7755	12504
124.987	0.7430	0.7751	12505
129.987	0.7772	0.7746	12506
139.992	0.8451	0.7738	12507
111.996	0.9141	1.1436	12402
114.994	0.9465	1.1432	12403
119.989	0.9997	1.1426	12404
129.987	1.1044	1.1413	12405
139.992	1.2075	1.1400	12406
115.993	1.2050	1.5135	8101
117.991	1.2348	1.5132	8102
119.989	1.2641	1.5128	8103
121.988	1.2932	1.5125	8104
123.987	1.3221	1.5121	8105
125.987	1.3510	1.5118	8106
127.987	1.3794	1.5114	8107
129.987	1.4080	1.5111	8108
131.987	1.4363	1.5107	8109
133.988	1.4645	1.5104	8110
135.989	1.4925	1.5101	8111
137.990	1.5206	1.5097	8112
139.992	1.5486	1.5094	8113
141.993	1.5765	1.5090	8114
143.995	1.6042	1.5087	8115
145.996	1.6319	1.5083	8116
147.998	1.6596	1.5080	8117
150.000	1.6871	1.5077	8118
155.005	1.7556	1.5068	8119
160.010	1.8237	1.5059	8120
165.014	1.8916	1.5051	8121
170.019	1.9592	1.5042	8122
175.024	2.0264	1.5033	8123
180.027	2.0936	1.5025	8124
185.030	2.1603	1.5016	8125
190.032	2.2268	1.5007	8126
195.034	2.2931	1.4998	8127
200.035	2.3592	1.4990	8128
210.033	2.4909	1.4972	8129
220.030	2.6218	1.4954	8130
220.030	2.6214	1.4954	8131
230.025	2.7517	1.4935	8132
240.020	2.8812	1.4917	8133
250.014	3.0103	1.4898	8134
260.008	3.1389	1.4880	8135
270.002	3.2670	1.4861	8136
279.997	3.3946	1.4842	8137
289.994	3.5216	1.4822	8138
299.992	3.6484	1.4803	8139
121.988	1.6805	2.1162	12601
124.987	1.7449	2.1154	12602
129.987	1.8504	2.1141	12603
134.988	1.9543	2.1129	12604
139.992	2.0568	2.1116	12605
144.995	2.1583	2.1104	12606
150.000	2.2589	2.1091	12607
125.987	2.0758	2.6479	7401
127.987	2.1314	2.6472	7402
129.987	2.1865	2.6466	7403
131.987	2.2411	2.6459	7404
133.988	2.2954	2.6453	7405
135.989	2.3491	2.6446	7406
137.990	2.4026	2.6440	7407
139.992	2.4558	2.6433	7408
141.993	2.5088	2.6427	7409
143.995	2.5614	2.6420	7410
145.996	2.6138	2.6414	7411
147.998	2.6659	2.6407	7412
150.000	2.7180	2.6401	7413
155.005	2.8470	2.6384	7414
160.010	2.9751	2.6368	7415
165.014	3.1021	2.6352	7416
170.019	3.2284	2.6336	7417
175.024	3.3538	2.6319	7418
180.027	3.4784	2.6303	7419
185.030	3.6024	2.6287	7420
190.032	3.7260	2.6270	7421
195.034	3.8486	2.6254	7422
195.034	3.8486	2.6254	7422
200.035	3.9711	2.6238	7423
210.033	4.2145	2.6204	7424
220.030	4.4562	2.6171	7425
230.025	4.6964	2.6138	7426
240.020	4.9347	2.6104	7427
230.025	4.6968	2.6140	7428
240.020	4.9356	2.6106	7429
250.014	5.1732	2.6072	7430
260.008	5.4093	2.6038	7431
270.002	5.6446	2.6004	7432
279.997	5.8785	2.5969	7433
289.994	6.1114	2.5933	7434
299.992	6.3432	2.5897	7435
129.987	2.6958	3.6637	7201
131.987	2.7788	3.6627	7202
133.988	2.8604	3.6617	7203
135.989	2.9410	3.6608	7204
137.990	3.0209	3.6598	7205
139.992	3.1001	3.6588	7206
141.993	3.1786	3.6579	7207
143.995	3.2565	3.6569	7208
145.996	3.3341	3.6560	7209
147.998	3.4110	3.6550	7210
150.000	3.4876	3.6540	7211
155.005	3.6773	3.6517	7212
160.010	3.8649	3.6493	7213
165.014	4.0507	3.6470	7214
170.019	4.2350	3.6446	7215
175.024	4.4179	3.6423	7216
180.027	4.5994	3.6399	7217
180.027	4.5995	3.6401	7218
185.030	4.7802	3.6378	7219
190.032	4.9597	3.6354	7220
195.034	5.1383	3.6330	7221
200.035	5.3160	3.6307	7222
210.033	5.6689	3.6259	7223
220.030	6.0188	3.6211	7224
230.025	6.3662	3.6163	7225
240.020	6.7110	3.6114	7226
250.014	7.0537	3.6065	7227
260.008	7.3946	3.6015	7228
270.002	7.7335	3.5966	7229
279.997	8.0706	3.5915	7230
289.994	8.4063	3.5865	7231
299.992	8.7404	3.5813	7232
150.000	3.9137	4.3084	8501
165.014	4.6013	4.2998	8502
180.027	5.2692	4.2913	8503
200.035	6.1393	4.2799	8504
230.025	7.4114	4.2626	8505
133.988	3.2925	4.7443	7001
135.989	3.4060	4.7430	7002
137.990	3.5176	4.7416	7003
139.992	3.6277	4.7403	7004
141.993	3.7366	4.7389	7005
143.995	3.8445	4.7376	7006
145.996	3.9514	4.7363	7007
147.998	4.0575	4.7350	7008
150.000	4.1629	4.7337	7009
155.005	4.4233	4.7304	7010
160.010	4.6804	4.7272	7011
165.014	4.9344	4.7240	7012
170.019	5.1861	4.7208	7013
175.024	5.4345	4.7176	7014
180.027	5.6819	4.7144	7015
185.030	5.9278	4.7113	7016
190.032	6.1719	4.7081	7017
195.034	6.4144	4.7049	7018
200.035	6.6558	4.7018	7019
210.033	7.1347	4.6954	7020
220.030	7.6091	4.6890	7021
210.033	7.1344	4.6952	7022
220.030	7.6091	4.6888	7023
230.025	8.0796	4.6824	7024
240.020	8.5464	4.6759	7025
250.014	9.0103	4.6693	7026
260.008	9.4713	4.6627	7027
270.002	9.9295	4.6560	7028
279.997	10.3848	4.6493	7029
289.994	10.8367	4.6425	7030
299.992	11.2872	4.6357	7031
137.990	3.7717	5.4871	8301
139.992	3.9057	5.4855	8302
141.993	4.0376	5.4839	8303
143.995	4.1679	5.4823	8304
145.996	4.2969	5.4808	8305
147.998	4.4249	5.4792	8306
150.000	4.5515	5.4776	8307
155.005	4.8645	5.4737	8308
160.010	5.1727	5.4699	8309
165.014	5.4770	5.4660	8310
170.019	5.7784	5.4622	8311
175.024	6.0765	5.4585	8312
180.027	6.3724	5.4547	8313
185.030	6.6661	5.4509	8314
190.032	6.9578	5.4471	8315
195.034	7.2477	5.4433	8316
200.035	7.5357	5.4395	8317
210.033	8.1071	5.4319	8318
220.030	8.6730	5.4242	8319
220.030	8.6718	5.4241	8320
230.025	9.2328	5.4165	8321
240.020	9.7891	5.4087	8322
250.014	10.3417	5.4008	8323
260.008	10.8902	5.3929	8324
270.002	11.4359	5.3849	8325
279.997	11.9776	5.3769	8326
289.994	12.5164	5.3687	8327
299.992	13.0526	5.3605	8328
137.990	3.9283	6.0824	6901
139.992	4.0827	6.0805	6902
141.993	4.2341	6.0787	6903
143.995	4.3832	6.0769	6904
145.996	4.5308	6.0751	6905
147.998	4.6767	6.0733	6906
150.000	4.8213	6.0715	6907
155.005	5.1779	6.0671	6908
160.010	5.5288	6.0627	6909
165.014	5.8752	6.0583	6910
170.019	6.2174	6.0540	6911
175.024	6.5565	6.0496	6912
180.027	6.8924	6.0453	6913
185.030	7.2260	6.0410	6914
190.032	7.5572	6.0366	6915
195.034	7.8860	6.0323	6916
200.035	8.2131	6.0279	6917
210.033	8.8617	6.0192	6918
220.030	9.5038	6.0105	6919
230.025	10.1405	6.0017	6920
240.020	10.7703	5.9929	6921
250.014	11.3966	5.9841	6922
260.008	12.0190	5.9751	6923
270.002	12.6373	5.9662	6924
279.997	13.2518	5.9571	6925
289.994	13.8633	5.9479	6926
299.992	14.4706	5.9387	6927
139.992	4.2052	6.5928	7801
141.993	4.3745	6.5908	7802
143.995	4.5407	6.5888	7803
145.996	4.7050	6.5868	7804
147.998	4.8670	6.5848	7805
150.000	5.0275	6.5828	7806
155.005	5.4232	6.5779	7807
160.010	5.8120	6.5730	7808
165.014	6.1955	6.5681	7809
170.019	6.5732	6.5633	7810
175.024	6.9484	6.5586	7811
180.027	7.3206	6.5538	7812
185.030	7.6898	6.5490	7813
190.032	8.0560	6.5442	7814
195.034	8.4200	6.5395	7815
200.035	8.7819	6.5346	7816
210.033	9.4992	6.5251	7817
220.030	10.2098	6.5154	7818
230.025	10.9136	6.5058	7819
230.025	10.9148	6.5061	7820
240.020	11.6123	6.4962	7821
250.014	12.3046	6.4862	7822
260.008	12.9920	6.4762	7823
270.002	13.6750	6.4661	7824
279.997	14.3536	6.4559	7825
289.994	15.0284	6.4456	7826
299.992	15.6989	6.4353	7827
139.992	4.2620	6.8747	2701
141.993	4.4415	6.8725	2702
143.995	4.6175	6.8704	2703
145.996	4.7909	6.8683	2704
147.998	4.9623	6.8662	2705
150.000	5.1318	6.8642	2706
155.005	5.5490	6.8590	2707
160.010	5.9593	6.8540	2708
165.014	6.3637	6.8489	2709
170.019	6.7637	6.8439	2710
175.024	7.1593	6.8389	2711
180.027	7.5515	6.8339	2712
185.030	7.9406	6.8290	2713
190.032	8.3270	6.8240	2714
195.034	8.7109	6.8190	2715
200.035	9.0924	6.8140	2716
210.033	9.8489	6.8040	2717
220.030	10.5977	6.7940	2718
230.025	11.3398	6.7839	2719
220.030	10.5990	6.7943	2720
230.025	11.3409	6.7842	2721
240.020	12.0771	6.7740	2722
250.014	12.8074	6.7638	2723
260.008	13.5329	6.7535	2724
270.002	14.2532	6.7430	2725
279.997	14.9689	6.7325	2726
289.994	15.6802	6.7219	2727
299.992	16.3876	6.7111	2728
141.993	4.5958	7.6840	7501
143.995	4.8006	7.6815	7502
145.996	5.0015	7.6791	7503
147.998	5.2001	7.6767	7504
150.000	5.3960	7.6743	7505
155.005	5.8780	7.6683	7506
160.010	6.3513	7.6624	7507
165.014	6.8179	7.6565	7508
170.019	7.2790	7.6507	7509
175.024	7.7353	7.6449	7510
180.027	8.1862	7.6392	7511
185.030	8.6352	7.6334	7512
190.032	9.0807	7.6276	7513
190.032	9.0802	7.6275	7514
195.034	9.5228	7.6217	7515
200.035	9.9626	7.6159	7516
210.033	10.8353	7.6043	7517
220.030	11.6987	7.5926	7518
230.025	12.5549	7.5808	7519
240.020	13.4022	7.5689	7520
250.014	14.2444	7.5570	7521
260.008	15.0797	7.5449	7522
270.002	15.9091	7.5327	7523
279.997	16.7342	7.5203	7524
289.994	17.5523	7.5078	7525
299.992	18.3667	7.4953	7526
185.030	8.9694	8.0302	8401
195.034	9.9172	8.0179	8402
210.033	11.3172	7.9994	8403
230.025	13.1530	7.9743	8404
143.995	4.9168	8.3819	11901
145.996	5.1430	8.3791	11902
147.998	5.3652	8.3764	11903
150.000	5.5847	8.3737	11904
155.005	6.1242	8.3671	11905
160.010	6.6540	8.3605	11906
165.014	7.1759	8.3539	11907
170.019	7.6922	8.3474	11908
175.024	8.2027	8.3409	11909
180.027	8.7093	8.3345	11910
185.030	9.2117	8.3280	11911
190.032	9.7107	8.3215	11912
195.034	10.2065	8.3150	11913
200.035	10.6993	8.3085	11914
210.033	11.6772	8.2955	11915
220.030	12.6444	8.2825	11916
210.033	11.6741	8.2952	11917
220.030	12.6416	8.2821	11918
230.025	13.5995	8.2689	11919
240.020	14.5502	8.2556	11920
250.014	15.4923	8.2422	11921
260.008	16.4281	8.2287	11922
270.002	17.3573	8.2151	11923
279.997	18.2803	8.2013	11924
289.994	19.1973	8.1874	11925
299.992	20.1092	8.1732	11926
141.993	4.7140	8.7499	3102
143.995	4.9677	8.7468	3103
145.996	5.2069	8.7439	3104
147.998	5.4421	8.7411	3105
150.000	5.6739	8.7382	3106
155.005	6.2440	8.7312	3107
160.010	6.8033	8.7243	3108
165.014	7.3548	8.7174	3109
170.019	7.9002	8.7105	3110
175.024	8.4399	8.7037	3111
180.027	8.9755	8.6969	3112
185.030	9.5067	8.6901	3113
190.032	10.0342	8.6833	3114
195.034	10.5584	8.6765	3115
200.035	11.0798	8.6697	3116
210.033	12.1133	8.6560	3117
220.030	13.1363	8.6423	3118
220.030	13.1341	8.6416	3119
230.025	14.1478	8.6278	3120
240.020	15.1530	8.6140	3121
250.014	16.1502	8.6000	3122
260.008	17.1403	8.5859	3123
270.002	18.1231	8.5717	3124
279.997	19.0990	8.5572	3125
289.994	20.0680	8.5426	3126
299.992	21.0320	8.5278	3127
143.995	4.9995	9.0187	8201
145.996	5.2489	9.0157	8202
147.998	5.4935	9.0127	8203
150.000	5.7349	9.0097	8204
155.005	6.3276	9.0024	8205
160.010	6.9099	8.9953	8206
165.014	7.4838	8.9881	8207
170.019	8.0512	8.9809	8208
175.024	8.6132	8.9738	8209
180.027	9.1705	8.9667	8210
185.030	9.7235	8.9596	8211
190.032	10.2729	8.9524	8212
195.034	10.8190	8.9453	8213
200.035	11.3619	8.9381	8214
143.995	4.9977	9.0186	8215
170.019	8.0504	8.9805	8216
200.035	11.3610	8.9378	8217
210.033	12.4354	8.9234	8218
220.030	13.5009	8.9090	8219
230.025	14.5573	8.8945	8220
240.020	15.6029	8.8798	8221
250.014	16.6415	8.8650	8222
260.008	17.6717	8.8501	8223
270.002	18.6956	8.8349	8224
279.997	19.7114	8.8197	8225
289.994	20.7215	8.8043	8226
143.995	5.0676	9.7709	7601
145.996	5.3447	9.7675	7602
147.998	5.6161	9.7641	7603
150.000	5.8835	9.7608	7604
155.005	6.5404	9.7527	7605
160.010	7.1858	9.7446	7606
165.014	7.8231	9.7366	7607
170.019	8.4535	9.7286	7608
175.024	9.0778	9.7206	7609
180.027	9.6972	9.7127	7610
185.030	10.3125	9.7047	7611
190.032	10.9239	9.6968	7612
195.034	11.5312	9.6888	7613
200.035	12.1356	9.6809	7614
210.033	13.3343	9.6649	7615
220.030	14.5208	9.6488	7616
230.025	15.6937	9.6326	7617
230.025	15.6950	9.6329	7618
240.020	16.8613	9.6166	7619
250.014	18.0166	9.6000	7620
260.008	19.1645	9.5833	7621
270.002	20.3049	9.5663	7622
143.995	5.1231	10.8686	8001
145.996	5.4415	10.8647	8002
147.998	5.7518	10.8608	8003
150.000	6.0578	10.8570	8004
155.005	6.8106	10.8477	8005
160.010	7.5519	10.8384	8006
165.014	8.2847	10.8291	8007
170.019	9.0106	10.8199	8008
175.024	9.7306	10.8108	8009
180.027	10.4459	10.8016	8010
185.030	11.1567	10.7925	8011
190.032	11.8630	10.7834	8012
195.034	12.5659	10.7742	8013
200.035	13.2650	10.7650	8014
210.033	14.6522	10.7466	8015
220.030	16.0262	10.7279	8016
230.025	17.3881	10.7092	8017
240.020	18.7385	10.6903	8018
250.014	20.0784	10.6712	8019
260.008	21.4083	10.6519	8020
145.996	5.5018	11.9244	7902
147.998	5.8491	11.9201	7903
150.000	6.1922	11.9159	7904
155.005	7.0392	11.9053	7905
160.010	7.8758	11.8948	7906
165.014	8.7053	11.8843	7907
170.019	9.5289	11.8739	7908
175.024	10.3471	11.8634	7909
180.027	11.1599	11.8530	7910
185.030	11.9686	11.8425	7911
190.032	12.7733	11.8321	7912
195.034	13.5742	11.8216	7913
200.035	14.3705	11.8111	7914
210.033	15.9527	11.7900	7915
220.030	17.5202	11.7687	7916
230.025	19.0742	11.7472	7917
240.020	20.6152	11.7254	7918
145.996	5.5529	13.4190	7701
147.998	5.9507	13.4141	7702
150.000	6.3460	13.4092	7703
155.005	7.3299	13.3969	7704
160.010	8.3087	13.3846	7705
165.014	9.2833	13.3724	7706
170.019	10.2538	13.3601	7707
175.024	11.2199	13.3478	7708
180.027	12.1821	13.3355	7709
185.030	13.1408	13.3232	7710
190.032	14.0952	13.3108	7711
195.034	15.0452	13.2983	7712
200.035	15.9911	13.2858	7713
210.033	17.8715	13.2606	7714
220.030	19.7353	13.2351	7715
230.025	21.5840	13.2092	7716
145.996	5.5803	14.4938	7301
147.998	6.0136	14.4884	7302
150.000	6.4479	14.4829	7303
155.005	7.5346	14.4693	7304
160.010	8.6223	14.4556	7305
165.014	9.7090	14.4418	7306
170.019	10.7932	14.4280	7307
175.024	11.8746	14.4143	7308
180.027	12.9527	14.4004	7309
185.030	14.0275	14.3865	7310
190.032	15.0986	14.3726	7311
195.034	16.1651	14.3586	7312
200.035	17.2279	14.3445	7313
210.033	19.3406	14.3161	7314
220.030	21.4361	14.2873	7315
145.996	5.6063	15.7701	7102
147.998	6.0859	15.7641	7103
150.000	6.5689	15.7580	7104
155.005	7.7889	15.7427	7105
160.010	9.0163	15.7272	7106
165.014	10.2477	15.7118	7107
170.019	11.4795	15.6962	7108
175.024	12.7098	15.6806	7109
180.027	13.9387	15.6650	7110
185.030	15.1641	15.6493	7111
190.032	16.3858	15.6335	7112
195.034	17.6042	15.6175	7113
200.035	18.8182	15.6015	7114
210.033	21.2328	15.5691	7115
145.996	5.6826	17.9228	11801
147.998	6.2544	17.9156	11802
150.000	6.8366	17.9083	11803
155.005	8.3181	17.8896	11804
160.010	9.8205	17.8706	11805
165.014	11.3329	17.8516	11806
170.019	12.8497	17.8324	11807
175.024	14.3668	17.8131	11808
180.027	15.8834	17.7937	11809
185.030	17.3973	17.7742	11810
190.032	18.9083	17.7545	11811
195.034	20.4147	17.7346	11812
145.996	5.7462	18.7458	11501
147.998	6.3635	18.7380	11502
150.000	6.9921	18.7301	11503
155.005	8.5924	18.7099	11504
160.010	10.2157	18.6895	11505
165.014	11.8507	18.6689	11506
170.019	13.4911	18.6482	11507
175.024	15.1326	18.6273	11508
180.027	16.7728	18.6063	11509
185.030	18.4107	18.5851	11510
190.032	20.0447	18.5637	11511
195.034	21.6738	18.5422	11512
150.000	7.2527	19.7940	9101
155.005	9.0246	19.7716	9102
160.010	10.8216	19.7489	9103
165.014	12.6306	19.7262	9104
170.019	14.4455	19.7032	9105
175.024	16.2603	19.6802	9106
180.027	18.0749	19.6569	9107
185.030	19.8847	19.6335	9108
190.032	21.6917	19.6097	9109
143.995	5.2963	20.6673	11401
145.996	6.0273	20.6582	11402
147.998	6.7749	20.6488	11403
150.000	7.5327	20.6392	11404
155.005	9.4574	20.6149	11405
160.010	11.4063	20.5904	11406
165.014	13.3667	20.5659	11407
170.019	15.3332	20.5411	11408
175.024	17.2983	20.5162	11409
180.027	19.2617	20.4911	11410
185.030	21.2213	20.4656	11411
143.995	5.5541	21.8571	11701
145.996	6.3880	21.8467	11702
147.998	7.2345	21.8361	11703
150.000	8.0903	21.8253	11704
155.005	10.2564	21.7981	11705
160.010	12.4430	21.7707	11706
165.014	14.6396	21.7433	11707
170.019	16.8381	21.7157	11708
175.024	19.0347	21.6877	11709
180.027	21.2276	21.6595	11710
143.995	5.5550	21.8658	11301
145.996	6.3896	21.8554	11302
147.998	7.2372	21.8448	11303
150.000	8.0928	21.8339	11304
155.005	10.2602	21.8066	11305
160.010	12.4475	21.7792	11306
165.014	14.6451	21.7516	11307
170.019	16.8455	21.7238	11308
175.024	19.0414	21.6959	11309
180.027	21.2361	21.6675	11310
141.993	5.0864	23.0236	6801
143.995	6.0185	23.0124	6802
145.996	6.9648	23.0006	6803
147.998	7.9207	22.9885	6804
150.000	8.8832	22.9762	6805
155.005	11.3096	22.9458	6806
160.010	13.7511	22.9154	6807
165.014	16.1970	22.8849	6808
170.019	18.6432	22.8541	6809
175.024	21.0844	22.8229	6810
139.992	4.6408	24.1656	11201
141.993	5.6875	24.1528	11202
143.995	6.7473	24.1395	11203
145.996	7.8162	24.1259	11204
147.998	8.8917	24.1123	11205
150.000	9.9710	24.0989	11206
155.005	12.6845	24.0653	11207
160.010	15.4054	24.0316	11208
165.014	18.1249	23.9977	11209
170.019	20.8398	23.9633	11210
137.990	4.3981	25.4197	11101
139.992	5.5916	25.4051	11102
141.993	6.7956	25.3899	11103
143.995	8.0063	25.3744	11104
145.996	9.2228	25.3591	11105
147.996	10.4416	25.3440	11106
150.000	11.6629	25.3290	11107
155.005	14.7193	25.2915	11108
160.010	17.7735	25.2537	11109
165.014	20.8210	25.2154	11110
135.989	4.2576	26.5253	6701
137.990	5.5957	26.5094	6702
139.992	6.9422	26.4921	6703
141.993	8.2923	26.4750	6704
143.995	9.6452	26.4584	6705
145.996	11.0021	26.4420	6706
147.998	12.3580	26.4255	6707
150.000	13.7136	26.4091	6708
155.005	17.1002	26.3679	6709
160.010	20.4746	26.3261	6710
135.989	6.1799	27.7894	8601
139.992	9.2435	27.7508	8602
145.996	13.8358	27.6951	8603
150.000	16.8861	27.6579	8604
131.987	3.1337	27.8278	3001
133.988	4.6569	27.8076	3002
135.989	6.1838	27.7893	3003
137.990	7.7142	27.7695	3004
139.992	9.2456	27.7509	3005
141.993	10.7772	27.7324	3006
143.995	12.3076	27.7139	3007
145.996	13.8350	27.6954	3008
147.998	15.3607	27.6769	3009
150.000	16.8833	27.6584	3010
155.005	20.6776	27.6116	3011
129.987	3.1750	28.7586	6601
131.987	4.8498	28.7366	6602
133.988	6.5264	28.7154	6603
135.989	8.2033	28.6953	6604
137.990	9.8768	28.6752	6605
139.992	11.5492	28.6552	6606
141.993	13.2188	28.6352	6607
143.995	14.8842	28.6153	6608
145.996	16.5472	28.5953	6609
147.998	18.2059	28.5752	6610
150.000	19.8604	28.5551	6611
152.002	21.5104	28.5348	6612
129.987	5.1513	29.5967	8701
133.988	8.7944	29.5529	8702
139.992	14.2282	29.4876	8703
147.998	21.4010	29.4005	8704
123.987	2.0663	30.5991	3301
125.987	4.0717	30.5717	3302
127.987	6.0736	30.5458	3303
129.987	8.0687	30.5223	3304
131.987	10.0571	30.4985	3305
133.988	12.0370	30.4748	3306
135.989	14.0095	30.4512	3307
137.990	15.9751	30.4277	3308
139.992	17.9331	30.4041	3309
141.993	19.8854	30.3804	3310
143.995	21.8300	30.3565	3311
123.987	2.5342	30.7537	11001
125.987	4.5717	30.7266	11002
127.987	6.6241	30.7009	11003
129.987	8.6274	30.6770	11004
131.987	10.6449	30.6528	11005
133.988	12.6542	30.6288	11006
135.989	14.6559	30.6048	11007
137.990	16.6506	30.5808	11008
139.992	18.6381	30.5568	11009
141.993	20.6167	30.5326	11010
121.988	2.1204	31.2838	6501
123.987	4.2621	31.2549	6502
125.987	6.3997	31.2282	6503
127.987	8.5275	31.2031	6504
129.987	10.6450	31.1779	6505
131.987	12.7562	31.1528	6506
133.988	14.8557	31.1280	6507
135.989	16.9441	31.1032	6508
137.990	19.0306	31.0783	6509
139.992	21.1040	31.0533	6510
119.989	2.0538	31.8837	10901
121.988	4.3243	31.8531	10902
123.987	6.5827	31.8252	10903
125.987	8.8306	31.7984	10904
127.987	11.0664	31.7717	10905
129.987	13.2909	31.7452	10906
131.987	15.5074	31.7189	10907
133.988	17.7116	31.6926	10908
135.989	19.9058	31.6661	10909
137.990	22.0927	31.6394	10910
119.989	2.0907	31.8967	9901
121.988	4.3610	31.8659	9902
123.987	6.6209	31.8379	9903
125.987	8.8700	31.8109	9904
127.987	11.1072	31.7840	9905
129.987	13.3333	31.7573	9906
131.987	15.5502	31.7308	9907
133.988	17.7548	31.7043	9908
135.989	19.9523	31.6777	9909
137.990	22.1410	31.6508	9910
117.991	1.8073	32.4138	5601
119.989	4.1910	32.3815	5602
121.988	6.5648	32.3525	5603
123.987	8.9247	32.3246	5604
125.987	11.2704	32.2967	5605
127.987	13.6024	32.2691	5606
129.987	15.9198	32.2416	5607
131.987	18.2273	32.2141	5608
133.988	20.5256	32.1863	5609
117.991	3.8594	32.8504	8801
121.988	8.8046	32.7903	8802
125.987	13.6829	32.7320	8803
131.987	20.9035	32.6457	8804
115.993	1.3862	32.8854	3501
117.991	3.8764	32.8507	3502
119.989	6.3523	32.8203	3503
121.988	8.8139	32.7911	3504
123.987	11.2577	32.7619	3505
125.987	13.6896	32.7332	3506
127.987	16.1053	32.7047	3507
129.987	18.5101	32.6761	3508
131.987	20.9029	32.6473	3509
113.995	1.4096	33.4281	2801
115.993	4.0243	33.3920	2802
117.991	6.6219	33.3603	2803
119.989	9.2038	33.3296	2804
121.988	11.7677	33.2990	2805
123.987	14.3135	33.2691	2806
125.987	16.8497	33.2396	2807
127.987	19.3713	33.2097	2808
129.987	21.8803	33.1795	2809
113.995	1.3999	33.4306	9301
115.993	4.0187	33.3942	9302
117.991	6.6221	33.3625	9303
119.989	9.2074	33.3315	9304
121.988	11.7742	33.3008	9305
123.987	14.3248	33.2707	9306
125.987	16.8605	33.2407	9307
127.987	19.3844	33.2106	9308
129.987	21.8939	33.1800	9309
111.996	1.2522	33.9215	6401
113.995	3.9918	33.8833	6402
115.993	6.7161	33.8504	6403
117.991	9.4152	33.8181	6404
119.989	12.0947	33.7862	6405
121.988	14.7578	33.7550	6406
123.987	17.4042	33.7239	6407
125.987	20.0399	33.6925	6408
127.987	22.6598	33.6609	6409
111.996	3.7877	34.3287	9401
113.995	6.6219	34.2945	9402
115.993	9.4336	34.2606	9403
117.991	12.2178	34.2276	9404
119.989	14.9846	34.1951	9405
121.988	17.7393	34.1625	9406
123.987	20.4747	34.1298	9407
109.998	0.9643	34.3721	3201
111.996	3.8173	34.3315	3202
113.995	6.6497	34.2974	3203
115.993	9.4560	34.2637	3204
117.991	12.2408	34.2307	3205
119.989	15.0052	34.1983	3206
121.988	17.7529	34.1658	3207
123.987	20.4844	34.1332	3208
108.000	1.8893	34.9904	9701
109.998	4.9055	34.9504	9702
111.996	7.8958	34.9153	9703
113.995	10.8562	34.8796	9704
115.993	13.7914	34.8451	.9705
117.991	16.7036	34.8109	9706
119.989	19.5986	34.7764	9707
121.988	22.4815	34.7415	9708
106.002	1.3049	35.3710	5301
108.000	4.4265	35.3281	5302
109.998	7.5173	35.2916	5303
111.996	10.5819	35.2546	5304
113.995	13.6157	35.2192	5305
115.993	16.6268	35.1841	5306
117.991	19.6241	35.1489	5307
119.989	22.6020	35.1132	5308
108.000	4.4294	35.3292	8901
111.996	10.5904	35.2558	8902
115.993	16.6385	35.1848	8903
119.989	22.6077	35.1134	8904
104.005	1.7569	35.8759	9801
106.002	5.0226	35.8326	9802
108.000	8.2535	35.7945	9803
109.998	11.4495	35.7565	9804
111.996	14.6184	35.7196	9805
113.995	17.7614	35.6826	9806
115.993	20.8837	35.6453	9807
102.008	0.9747	36.2163	5501
104.005	4.3398	36.1697	5502
106.002	7.6717	36.1303	5503
108.000	10.9641	36.0910	5504
109.998	14.2237	36.0531	5505
111.996	17.4597	36.0153	5506
113.995	20.6766	35.9771	5507
102.008	1.2377	36.2449	5701
104.005	4.6118	36.1990	5702
106.002	7.9501	36.1594	5703
108.000	11.2504	36.1203	5704
109.998	14.5134	36.0819	5705
111.996	17.7568	36.0440	5706
113.995	20.9811	36.0056	5707
102.008	3.9537	36.5444	9501
104.005	7.4001	36.5033	9502
106.002	10.7999	36.4627	9503
108.000	14.1678	36.4237	9504
109.998	17.5067	36.3846	9505
111.996	20.8277	36.3452	9506
100.010	0.4947	36.5951	2901
102.008	3.9704	36.5447	2902
104.005	7.4128	36.5043	2903
106.002	10.8108	36.4638	2904
108.000	14.1772	36.4249	2905
109.998	17.5172	36.3861	2906
111.996	20.8393	36.3469	2907
98.012	0.8850	37.0590	5101
100.010	4.5114	37.0089	5102
102.008	8.0937	36.9662	5103
104.005	11.6289	36.9252	5104
106.002	15.1285	36.8847	5105
108.000	18.6042	36.8442	5106
109.998	22.0614	36.8031	5107
98.012	4.9668	37.4461	9201
102.008	12.3521	37.3597	9202
104.005	15.9787	37.3177	9203
106.002	19.5824	37.2755	9204
108.000	23.1667	37.2326	9205
94.013	1.3101	37.9022	10001
96.013	5.2104	37.8533	10002
98.012	9.0596	37.8054	10003
100.010	12.8559	37.7618	10004
102.008	16.6183	37.7182	10005
104.005	20.3521	37.6744	10006
94.013	1.3182	37.9060	5001
96.013	5.2200	37.8572	5002
98.012	9.0684	37.8094	5003
100.010	12.8621	37.7659	5004
102.008	16.6237	37.7225	5005
104.005	20.3536	37.6789	5006
92.012	1.6868	38.3248	9601
94.013	5.7328	38.2752	9602
96.013	9.7164	38.2263	9603
98.012	13.6445	38.1812	9604
100.010	17.5364	38.1360	9605
102.008	21.4026	38.0904	9606
90.010	0.9805	38.6564	5201
92.012	5.1494	38.6036	5202
94.013	9.2524	38.5525	5203
96.013	13.2953	38.5062	5204
98.012	17.3028	38.4601	5205
100.010	21.2828	38.4135	5206
90.010	4.7415	38.9389	9001
94.013	13.1362	38.8416	9002
98.012	21.3414	38.7459	9003
88.005	0.4645	39.0005	4601
90.010	4.7619	38.9402	4602
92.012	8.9965	38.8907	4603
94.013	13.1625	38.8431	4604
96.013	17.2837	38.7957	4605
98.012	21.3782	38.7476	4606
86.000	0.3367	39.3667	3401
88.005	4.7559	39.3037	3402
90.010	9.1085	39.2529	3403
92.012	13.3967	39.2040	3404
94.013	17.6480	39.1552	3405
96.013	21.8622	39.1059	3406
88.005	4.7505	39.3046	10101
90.010	9.1162	39.2535	10102
92.012	13.4113	39.2043	10103
94.013	17.6633	39.1551	10104
96.013	21.8822	39.1052	10105
83.995	0.4459	39.7405	10501
86.000	5.0134	39.6764	10502
88.005	9.5029	39.6242	10503
90.010	13.9204	39.5735	10504
92.012	18.3051	39.5229	10505
94.013	22.6595	39.4713	10506
83.995	0.4651	39.7423	4501
86.000	5.0379	39.6788	4502
88.005	9.5411	39.6268	4503
90.010	13.9741	39.5764	4504
92.012	18.3629	39.5259	4505
94.013	22.7325	39.4744	4506
81.992	0.4370	40.1067	10801
83.995	5.1394	40.0403	10802
86.000	9.7620	39.9880	10803
88.005	14.3199	39.9359	10804
90.010	18.8417	39.8836	10805
92.012	23.3386	39.8303	10806
81.992	0.4377	40.1072	4201
83.995	5.1391	40.0409	4202
86.000	9.7704	39.9887	4203
88.005	14.3384	39.9367	4204
90.010	18.8670	39.8846	4205
92.012	23.3699	39.8314	4206
79.991	0.4890	40.4642	10201
81.992	5.3375	40.3965	10202
83.995	10.0991	40.3430	10203
86.000	14.7862	40.2894	10204
88.005	19.4396	40.2353	10205
79.991	0.4945	40.4640	4401
81.992	5.3375	40.3965	4402
83.995	10.0956	40.3432	4403
86.000	14.7864	40.2897	4404
88.005	19.4439	40.2359	4405
77.991	1.4832	40.8761	10301
79.991	6.4748	40.8127	10302
81.992	11.3732	40.7571	10303
83.995	16.2170	40.7016	10304
86.000	21.0321	40.6455	10305
75.993	1.6279	41.2328	6301
77.991	6.7642	41.1688	6302
79.991	11.7882	41.1121	6303
81.992	16.7735	41.0553	6304
83.995	21.7365	40.9977	6305
73.996	0.4564	41.5151	4301
75.993	5.7320	41.4434	4302
77.991	10.8956	41.3856	4303
79.991	15.9845	41.3278	4304
81.992	21.0491	41.2691	4305
73.996	0.4815	41.5190	10601
75.993	5.7438	41.4471	10602
77.991	10.8992	41.3889	10603
79.991	15.9884	41.3308	10604
81.992	21.0641	41.2719	10605
73.996	0.5595	41.5209	10401
75.993	5.8320	41.4497	10402
77.991	10.9885	41.3914	10403
79.991	16.0681	41.3333	10404
81.992	21.1332	41.2744	10405
71.998	0.8278	41.8772	6101
73.996	6.2426	41.8068	6102
75.993	11.5453	41.7467	6103
77.991	16.7781	41.6867	6104
79.991	21.9801	41.6259	6105
70.000	0.4372	42.1990	10701
71.998	6.0066	42.1238	10702
73.996	11.4350	42.0624	10703
75.993	16.8041	42.0012	10704
77.991	22.1545	41.9388	10705
70.000	0.4585	42.1996	4101
71.998	6.0266	42.1252	4102
73.996	11.4696	42.0640	4103
75.993	16.8566	42.0028	4104
77.991	22.2168	41.9406	4105
68.001	0.8566	42.5531	6001
70.000	6.5671	42.4798	6002
71.998	12.1452	42.4164	6003
73.996	17.6633	42.3532	6004
75.993	23.1733	42.2884	6005
66.000	0.8508	42.8768	5901
68.001	6.7269	42.8021	5902
70.000	12.4546	42.7372	5903
71.998	18.1377	42.6724	5904
73.996	23.7925	42.6058	5905
63.999	0.9133	43.2041	5401
66.000	6.9342	43.1279	5402
68.001	12.8113	43.0610	5403
70.000	18.6316	42.9941	5404
63.999	1.2662	43.2189	4901
66.000	7.2989	43.1446	4902
68.001	13.1924	43.0780	4903
70.000	19.0462	43.0114	4904
61.998	1.2361	43.5478	5801
63.999	7.4169	43.4718	5802
66.000	13.4638	43.4033	5803
68.001	19.4467	43.3348	5804
59.999	0.5011	43.8506	4701
61.998	6.8268	43.7690	4702
63.999	13.0040	43.6990	4703
66.000	19.1342	43.6290	4704
59.999	0.5139	43.8515	11601
61.998	6.8361	43.7701	11602
63.999	13.0332	43.7001	11603
66.000	19.1699	43.6300	11604
58.002	1.5812	44.2038	4801
59.999	8.0600	44.1262	4802
61.998	14.4207	44.0544	4803
63.999	20.7475	43.9822	4804
56.005	1.4389	44.5234	6201
58.002	8.0623	44.4435	6202
59.999	14.5535	44.3698	6203
61.998	21.0109	44.2954	6204
56.005	4.8597	44.6360	12201
58.002	11.4722	44.5618	12202
59.999	18.0087	44.4877	12203
61.998	24.5494	44.4105	12204
53.610	1.3141		12001
53.709	2.3350		12002
53.809	3.3653		12003
53.909	4.3943		12004
54.009	5.0652	44.9752	12005
54.109	5.4099	44.9721	12006
54.209	5.7571	44.9682	12007
55.007	8.5036	44.9373	12008
56.005	11.8881	44.8989	12009
58.002	18.5846	44.8229	12010
53.909	4.3901		12101
54.009	5.4182		12102
54.109	6.4487		12103
54.209	7.4857		12104
54.309	8.5322		12105
54.408	9.5650		12106
54.508	10.6060		12107
54.608	11.6500		12108
54.708	12.6979		12109
54.808	13.7392		12110
54.907	14.7088	45.1393	12111
55.007	15.0681	45.1353	12112
55.107	15.4160	45.1315	12113
56.005	18.4968	45.0966	12114

All experimental single-phase PVT data in both the compressed liquid and vapor regions are given in table 1. The column of this table labeled “IDENT” contains the identification number of each data point. The last two digits represent the point number while the remaining digits are the number of the run or experimental isochore. Entries in runs 120 and 121 which contain no value for the density are pressures measured on the melting curve. Experimental PVT data for densities less than 0.22 mol/1 were obtained indirectly, since gas expansion measurements at these low densities were not possible. Pressures were obtained using an air deadweight gage while the density was obtained by heating the PVT cell to 175 K using an extrapolation of the previously determined pressure-density relationship for that isotherm obtained from higher density measurements.

The estimated accuracy of the density measurements is 0.1 percent. However, the corresponding precision is better, indicated by the fact that the standard deviation of all PVT data from eqs (1) and (5) is approximately 0.02 percent in density.

The purity of the fluorine sample used for these measurements was 99.99 percent as determined from residual gas analysis after reaction of fluorine with mercury.

3. Representation of PVT Data

No single equation of state was found capable of representing the data to within its precision. Therefore, to obtain the best possible representation of all the data for computation of thermodynamic functions, the PVT surface was divided into two regions as pictured in figure 1. The data in each region were correlated separately as discussed below.

Figure 1.

Density-temperature diagram showing the regions used for representation of the PVT data.

3.1. Low-Density Region

All experimental PVT data at densities less than 6.0 mol/1 were represented by the truncated virial equation

$$P=RT\left[\rho +B\left(T\right){\rho }^2+C\left(T\right){\rho }^3\right]$$ (1)

where R = 8.3143 J/mol — K. The decision to use 6.0 mol/1 as a maximum density value for the virial surface was based on the results obtained by fitting the experimental data to eq (1). By varying the maximum experimental density included in the fit of the virial equation, the data were found to exhibit definite systematic deviations in density as well as temperature for all densities greater than 6.0 mol/1. Equation (1) was based on 329 PVT data points in the virial region. Further, 26 measured specific heat (C_v) data points [9] between 6.5 and 6.8 mol/1 at temperatures from 140 K to 300 K were compared to C_v values calculated from the virial equation and the ideal gas values, $C_v^{\circ }$ [8]. The reason for this was to ascertain that the apparent deviations, being of the order of 1.5 percent, were fairly constant and not a function of temperature.

The second and third virial coefficients were represented by

$$B(T)=\sum _{i=1}^5{B}_i{T}^{(1-i)/4}$$ (1a)

and

$$C(T)=\sum _{i=1}^6{C}_i{T}^{(1-i)/2},$$ (1b)

respectively. An iterative method was used to optimize both the number of coefficients of B(T) and C(T) and their temperature dependence. The coefficients of eqs (1a) and (1b) and their significance level obtained through a weighted least-squares fit of all PVT data in this region are given in table 2. Weight factors, W, used in the fitting of eq (1) were defined as

$$W=\frac{1}{{\sigma }_p^2+{\left(\frac{\partial P}{\partial \rho }{\sigma }_{\rho }\right)}^2+{\left(\frac{\partial P}{\partial T}{\sigma }_T\right)}^2}$$ (2)

where ${\sigma }_p^2,{\sigma }_{\rho }^2,{\sigma }_T^2$ are the respective variances in pressure, density, and temperature. PVT data below 100 K were weighted relatively less than above this temperature, as the uncertainty of the measurements in this region increases rapidly with decreasing density. The weighted standard deviation in density between the virial surface and all of the 329 PVT data points is 0.041 percent. For consistency eq (1) was constrained to give the proper saturation temperature (137.327 K) for the 6.0 mol/1 isochore [2].

Table 2. Least squares estimate of the coefficients of eqs (1a) and (1b).

Coefficient	Least squares estimate of coefficient	Standard deviation of coefficient	Significance level in percenta
B1	−4.43719523	1.10	99.9+
B2	6.88646977 × 10	1.61 × 10	99.9+
B3	−4.00652537 × 102	8.85 × 10	99.9+
b4	1.04730534 × 103	2.15 × 102	99.9+
b5	−1.05492603 × 103	1.96 × 102	99.9+
C1	3.97288149 × 10−1	6.38 × 10−2	99.9+
C2	−2.80769183 × 10	4.33	99.9+
C3	7.95698766 × 102	1.18 × 102	99.9+
C4	−1.12867697 × 104	1.59 × 103	99.9+
C5	8.01450388 × 104	1.08 × 104	99.9+
C6	−2.27594177 × 105	2.93 × 104	99.9+

^aThese parameters are significant at the level indicated when applying the standard F-test.

The second and third virial coefficients, calculated from eqs (1a) and (1b), are given in table 3. Also given in this table are the quantities δB and δC, which are the respective estimated uncertainties of the coefficients based on experience gained when fitting the virial surface. A comparison of the second virial coefficient with values obtained by White, Hu, and Johnston [10] is given in figure 2. In the calculation of their data these authors neglected the contribution of the third and higher order virial coefficients, which is the probable reason for their larger negative values, especially at lower temperatures. Temperature scale differences could also account for part of the deviations. Since the data from reference [10] do not represent just the second virial coefficient, further comparisons with eq (1a) were made by converting values from oxygen [11] and argon [12] using corresponding states approach based on critical parameters as follows:

$$B_{\text{ converted }}=B(X)\frac{{\rho }_c(X)}{{\rho }_c\left(F_2\right)}$$ (3)

and

$$T_{\text{ converted }}=T(X)\frac{T_c\left(F_2\right)}{T_c(X)}$$ (4)

where X represents either oxygen or argon. The agreement is good as may be seen from figure 2. In fact, the correspondence between values calculated from the second virial coefficient of oxygen and eq (1a) is better than one may justifiably expect from the principle of corresponding states.

Table 3. Second and third virial coefficients of fluorine.

(δB and δC are estimated uncertainties)

T	B	δB × 103	C	δC × 103
K	l/mol	l/mol	l/mol2	(l/mol)2
80	−0.2396	40	−0.022557	20
85	−.2132		−.013548
90	−.1910		−.007748
95	−.1722		−.004016
100	−.1561	10	−.001624	3
105	−.1422		−.000106
110	−.1301		.000838
115	−.1194		.001409
120	−.1100		.001736
125	−.1017	2	.001905	0.5
130	−.0942		.001973
135	−.0875		.001979
140	−.0815		.001947
145	−.0759		.001893
150	−.0709	0.3	.001828	.03
155	−.0663		.001758
160	−.0621		.001689
165	−.0582		.001621
170	−.0546		.001557
175	−.0512		.001498
180	−.0481		.001442
185	−.0452		.001391
190	−.0425		.001344
195	−.0400		.001301
200	−.0376	.3	.001261	.03
205	−.0354		.001224
210	−.0332		.001190
215	−.0313		.001159
220	−.0294		.001130
225	−.0276		.001104
230	−.0259		.001080
235	−.0243		.001057
240	−.0228		.001037
245	−.0214		.001019
250	−.0200	.3	.001003	.03
255	−.0187		.000988
260	−.0175		.000976
265	−.0163		.000966
270	−.0152		.000957
275	−.0141		.000951
280	−.0131		.000947
285	−.0122		.000946
290	−.0112		.000946
295	−.0104		.000949
300	−.0095	.3	.000955	.04

Figure 2.

Comparisons of second virial coefficients of fluorine.

3.2. High-Density Region

a. Isotherm Representation

The isotherms in the high-density region (see fig. 1) were represented by polynomials of the form

$$P=RT\rho +\sum _{i=1}^n{A}_i{\rho }^{i-1},$$ (5)

where A₁ = A₂ = 0 for T > T_c or p < p_c. No more than 3 coefficients were used for the isotherms below 60 K since these consisted of only 4 P — p data points each. As many as 9 coefficients were necessary for the 146 K and 148 K isotherms (slightly above the critical temperature) to adequately represent the data. From 4 to 7 coefficients were needed to represent all of the remaining isotherms. The isotherms in the compressed liquid and vapor phases below the critical temperature were constrained to the corresponding saturation density from reference [2] (see also Appendix). Above 138 K the isotherms were also fitted to the low density data in the virial region to provide a better match of the surfaces around the 6.0 mol/1 isochore.

The standard deviation of the 381 experimental data points in the compressed liquid was only 0.005 percent while the 540 compressed vapor data points exhibit a larger deviation of 0.018 percent. The latter value is higher due mainly to the contribution from the isotherms just above the critical temperature where the deviations are much larger than over the rest of the surface.

b. Isochore Representation

Many calculations of thermodynamic properties require knowledge of the derivatives (∂P/∂T)_p and (∂²P/∂T²)_p. In the low-density region these derivatives may be calculated directly from eq (1). For densities above 6.0 mol/1 it was first necessary to derive true isochores by calculating pressures at even density increments using the isotherm representations. Density increments of 0.5 mol/1 were used for the 80 isochores between 5.5 and 45.0 mol/1. The true isochores were then represented using functions of the form

$$P=\sum _{i=1}^n{A}_i{T}^{(3-2i)}.$$ (6)

The number of terms² of eq (6) varied from 7 at the lowest density to 3 at the 45.0 mol/1 isochore. The good fit of the isotherms was directly carried over in the correlation of these isochores.

4. Derived Properties

4.1. Densities of the Liquid at Freezing

Density calculations of the PVT surface below 56 K were obtained by extrapolating isobars computed from the isotherms between 56 K and 64 K. The density of the liquid in equilibrium with the solid derived from the intersections of these isobars with the melting curve, reference [3], was expressed as a function of either temperature or pressure by

$${\rho }_{\text{ melt }L}={\rho }_t+0.208\left(T-T_t\right), mol /1$$ (7)

or

$${\rho }_{\text{ melt }}L={\rho }_t+0.020P\left(\text{MN}/{\text{m}}^2\right).$$ (8)

A value of 44.86₂ mol/1 was used for the liquid density, p_t, at the triple point.

4.2. The Joule-Thomson Inversion Curve

Calculated points on the Joule-Thomson inversion curve are given in table 4. This curve is defined as the locus of points where the Joule-Thomson coefficient is equal to zero. This condition may be described in classical thermodynamics by the relationship

$$\frac{-T}{{\rho }^2}{\left(\frac{\partial \rho }{\partial T}\right)}_p=\frac{1}{\rho }$$ (9)

or more conveniently

$$T{\left(\frac{\partial P}{\partial T}\right)}_{\rho }=\rho {\left(\frac{\partial P}{\partial \rho }\right)}_T$$ (10)

Table 4. The Joule-Thomson inversion curve.

T	P	Density	APa
K	MN/m2	Mol/l	MN/m2
118	2.732	32.615	0.19
120	4.340	32.411	0.21
122	6.092	32.250	0.22
124	7.649	32.058	0.23
126	9.288	31.895	0.23
128	10.861	31.727	0.25
130	12.373	31.556	0.25
132	13.824	31.381	0.26
134	15.278	31.214	0.26
136	16.583	31.024	0.28
138	17.980	30.864	0.27
140	19.155	30.664	0.26
142	20.811	30.573	0.31
144	21.668	30.322	0.31

^aThese estimated pressure errors are due to a 1 percent assumed uncertainty in either the isotherm or the isochore derivative.

Equation (10) was solved by an iterative technique using the isotherm derivatives, (∂P/∂p)_T, and the isochore derivatives, (∂P/∂T)_p, obtained from eqs (5) and (6), respectively. The computed pressure errors in table 4 are based on an assumed uncertainty of 1 percent in these derivatives. No published Joule-Thomson data for fluorine are available for comparison to values tabulated in table 4. However, a comparison with oxygen [11] and argon [12] using the theory of corresponding states based on critical parameters, is given in figure 3.

Figure 3.

Comparisons of reduced Joule-Thomson inversion curves of fluorine, oxygen, and argon.

5. Appendix

Given below are correlations for different properties of fluorine as reported earlier. The number of significant figures given for the coefficients is not justified on the basis of the uncertainty of the data, but are presented to enable duplication of the calculated values.

Vapor Pressure

The following vapor pressure equation was presented in reference [2]:

$$\text{ln}\left(\frac{P}{P_t}\right)=A_{1}X+A_2{X}^2+A_3{X}^3+A_{4}X{(1-X)}^{A_5}$$ (11)

where $X=\left(1-T_t/T\right)/\left(1-T_t/T_c\right)$ and

• A₁= 7.89592346

• A₂= 3.38765063

• A₃= −1.34590196

• A₄= 2.73138936

• A₅= 1.4327

• P_t= 2.52 × 10⁻⁴ MN/m²

• T_t= 53.4811 K

• T_c= 144.31 K.

Saturated Liquid Densities

The saturated liquid densities, p_l, were described in [2] with the argument Z = 1 — T/T_c, as

$$\left(\frac{{\rho }_l-{\rho }_c}{{\rho }_c}\right)=B_1{Z}^{0.35}+\sum _{i=2}^6{B}_i{Z}^{i-1}$$ (12)

where

• B₁= 1.81881076

• B₂= 8.75236491 × 10⁻¹

• B₃= −8.50458910 × 10⁻¹

• B₄= 1.37284761

• B₅= −1.01331503

• B₆= 2.73840128 × 10⁻¹

• p_c= 15.10 mol/1

• T_c= 144.31 K

Saturated Vapor Density

The saturated vapor densities, p_y, were reported by reference [2] as

$$\text{ln}\left(\frac{{\rho }_g}{{\rho }_c}\right)=C_1\left(\frac{Z}{Z-1}\right)+C_2{Z}^{0.35}+\sum _{i=3}^7{C}_i{Z}^{i-2}$$ (13)

with the argument, Z, as given above. The coefficients are

• C_{1 =} 4.85547085

• C_{2 =} −1.96015519

• C_{3 =} −1.88066900 ×10⁻¹

• C_{4 =} 6.21165939

• C_{5 =} −2.29600897 × 10¹

• C_{6 =} 4.69524623 × 10¹

• C_{7 =} −4.30650270 × 10¹

The Melting Curve

Straty and Prydz [3] represented the pressures along the solid-liquid melting curve as

$$P=P_t+P_0\left[{\left(\frac{T}{T_c}\right)}^C-1\right]$$ (14)

where

$$P_0=249.975{\text{ MN/m}}^{\text{2}}$$

$$c=2.1845,$$

and the other variables as defined above.