Russell J. Donnelly
541-346-4226 (Tel)
541-346-5861 (Fax)
Table 1 : : 2 : : 3 : : 4 : : 5
The
Calculated Thermodynamic Properties of Superfluid Helium-4
James S. Brooks and Russell J. Donnelly
| Table 11. . Specific heat at constant volume (J g-1 K-1) | |||||||||||
| Temp. | Pressure (atm) | ||||||||||
| (K) | .00 | 2.50 | 5.00 | 7.50 | 10.00 | 12.50 | 15.00 | 17.50 | 20.00 | 22.50 | 25.00 |
0.10 |
2.0597E-5 |
1.5930E-5 |
1.2912E-5 |
1.0798E-5 |
9.2471E-6 |
8.0639E-6 |
7.1329E-6 |
6.3825E-6 |
5.7664E-6 |
5.2515E-6 |
4.8151E-6 |
| 0.15 | 6.8827E-5 | 5.3569E-5 | 4.3498E-5 | 3.6449E-5 | 3.1241E-5 | 2.7256E-5 | 2.4116E-5 | 2.1583E-5 | 1.9494E-5 | 1.7747E-5 | 1.6263E-5 |
| 0.20 | 1.6143E-4 | 1.2631E-4 | 1.0296E-4 | 8.6429E-5 | 7.4178E-5 | 6.4773E-5 | 5.7348E-5 | 5.1350E-5 | 4.6413E-5 | 4.2283E-5 | 3.8781E-5 |
| 0.25 | 3.1144E-4 | 2.4535E-4 | 2.0075E-4 | 1.6891E-4 | 1.4516E-4 | 1.2687E-4 | 1.1239E-4 | 1.0068E-4 | 9.1019E-5 | 8.2932E-5 | 7.6069E-5 |
| 0.30 | 5.3134E-4 | 4.2159E-4 | 3.4639E-4 | 2.9216E-4 | 2.5148E-4 | 2.2000E-4 | 1.9501E-4 | 1.7475E-4 | 1.5802E-4 | 1.4400E-4 | 1.3208E-4 |
| 0.35 | 8.3306E-4 | 6.6581E-4 | 5.4948E-4 | 4.6471E-4 | 4.0070E-4 | 3.5098E-4 | 3.1140E-4 | 2.7928E-4 | 2.5274E-4 | 2.3051E-4 | 2.1171E-4 |
| 0.40 | 1.2284E-3 | 9.8937E-4 | 8.2061E-4 | 6.9653E-4 | 6.0239E-4 | 5.2919E-4 | 4.7097E-4 | 4.2401E-4 | 3.8581E-4 | 3.5472E-4 | 3.2915E-4 |
| 0.45 | 1.7327E-3 | 1.4077E-3 | 1.1760E-3 | 1.0058E-3 | 8.7705E-4 | 7.7782E-4 | 7.0118E-4 | 6.4130E-4 | 5.9556E-4 | 5.6182E-4 | 5.3959E-4 |
| 0.50 | 2.3749E-3 | 1.9530E-3 | 1.6557E-3 | 1.4403E-3 | 1.2825E-3 | 1.1677E-3 | 1.0838E-3 | 1.0280E-3 | 9.9665E-4 | 9.8834E-4 | 1.0069E-3 |
| 0.55 | 3.2200E-3 | 2.7068E-3 | 2.3569E-3 | 2.1210E-3 | 1.9642E-3 | 1.8694E-3 | 1.8204E-3 | 1.8147E-3 | 1.8535E-3 | 1.9388E-3 | 2.0859E-3 |
| 0.60 | 4.4293E-3 | 3.8393E-3 | 3.4840E-3 | 3.2928E-3 | 3.2148E-3 | 3.2156E-3 | 3.2847E-3 | 3.4256E-3 | 3.6485E-3 | 3.9671E-3 | 4.3823E-3 |
| 0.65 | 6.2754E-3 | 5.6529E-3 | 5.3993E-3 | 5.3742E-3 | 5.5071E-3 | 5.7552E-3 | 6.0901E-3 | 6.5498E-3 | 7.1342E-3 | 7.8673E-3 | 8.7987E-3 |
| 0.70 | 9.1734E-3 | 8.6487E-3 | 8.6463E-3 | 9.0030E-3 | 9.5489E-3 | 1.0265E-2 | 1.1075E-2 | 1.2077E-2 | 1.3259E-2 | 1.4747E-2 | 1.6498E-2 |
| 0.75 | 1.3830E-2 | 1.3472E-2 | 1.4016E-2 | 1.5026E-2 | 1.6267E-2 | 1.7726E-2 | 1.9328E-2 | 2.1161E-2 | 2.3310E-2 | 2.5873E-2 | 2.8820E-2 |
| 0.80 | 2.1058E-2 | 2.1079E-2 | 2.2425E-2 | 2.4426E-2 | 2.6776E-2 | 2.9301E-2 | 3.2024E-2 | 3.5021E-2 | 3.8572E-2 | 4.2554E-2 | 4.7252E-2 |
| 0.85 | 3.1759E-2 | 3.2527E-2 | 3.5068E-2 | 3.8408E-2 | 4.2234E-2 | 4.6237E-2 | 5.0424E-2 | 5.5037E-2 | 6.0280E-2 | 6.6287E-2 | 7.3208E-2 |
| 0.90 | 4.7598E-2 | 4.9215E-2 | 5.3154E-2 | 5.8245E-2 | 6.3830E-2 | 6.9690E-2 | 7.5851E-2 | 8.2618E-2 | 8.9913E-2 | 9.8511E-2 | 1.0767E-1 |
| 0.95 | 7.0005E-2 | 7.2512E-2 | 7.8023E-2 | 8.5160E-2 | 9.2937E-2 | 1.0092E-1 | 1.0950E-1 | 1.1869E-1 | 1.2873E-1 | 1.4003E-1 | 1.5225E-1 |
| 1.00 | 1.0504E-1 | 1.0893E-1 | 1.1564E-1 | 1.2418E-1 | 1.3393E-1 | 1.4449E-1 | 1.5582E-1 | 1.6797E-1 | 1.8135E-1 | 1.9588E-1 | 2.1193E-1 |
| 1.05 | 1.4650E-1 | 1.5145E-1 | 1.5916E-1 | 1.6919E-1 | 1.8117E-1 | 1.9456E-1 | 2.0916E-1 | 2.2482E-1 | 2.4177E-1 | 2.6007E-1 | 2.8043E-1 |
| 1.10 | 1.9816E-1 | 2.0456E-1 | 2.1342E-1 | 2.2498E-1 | 2.3926E-1 | 2.5576E-1 | 2.7380E-1 | 2.9383E-1 | 3.1497E-1 | 3.3814E-1 | 3.6419E-1 |
| 1.15 | 2.6074E-1 | 2.6933E-1 | 2.8047E-1 | 2.9375E-1 | 3.0938E-1 | 3.2762E-1 | 3.4867E-1 | 3.7315E-1 | 4.0014E-1 | 4.2974E-1 | 4.6027E-1 |
| 1.20 | 3.3523E-1 | 3.4559E-1 | 3.5856E-1 | 3.7445E-1 | 3.9314E-1 | 4.1524E-1 | 4.4072E-1 | 4.6971E-1 | 5.0271E-1 | 5.3958E-1 | 5.8045E-1 |
| 1.25 | 4.2128E-1 | 4.3523E-1 | 4.5245E-1 | 4.7252E-1 | 4.9550E-1 | 5.2151E-1 | 5.5174E-1 | 5.8598E-1 | 6.2517E-1 | 6.6976E-1 | 7.1924E-1 |
| 1.30 | 5.2642E-1 | 5.4326E-1 | 5.6513E-1 | 5.9076E-1 | 6.1995E-1 | 6.5259E-1 | 6.9020E-1 | 7.3168E-1 | 7.7802E-1 | 8.3001E-1 | 8.8619E-1 |
| 1.35 | 6.5752E-1 | 6.7786E-1 | 7.0383E-1 | 7.3540E-1 | 7.7206E-1 | 8.1347E-1 | 8.6039E-1 | 9.1158E-1 | 9.6938E-1 | 1.0339E0 | 1.1076E0 |
| 1.40 | 8.0923E-1 | 8.3311E-1 | 8.6374E-1 | 9.0075E-1 | 9.4394E-1 | 9.9358E-1 | 1.0497E0 | 1.1124E0 | 1.1844E0 | 1.2653E0 | 1.3577E0 |
| 1.45 | 9.7015E-1 | 9.9588E-1 | 1.0293E0 | 1.0725E0 | 1.1243E0 | 1.1846E0 | 1.2506E0 | 1.3231E0 | 1.4038E0 | 1.4981E0 | 1.6116E0 |
| 1.50 | 1.1334E0 | 1.1626E0 | 1.2003E0 | 1.2508E0 | 1.3128E0 | 1.3841E0 | 1.4619E0 | 1.5459E0 | 1.6373E0 | 1.7451E0 | 1.8818E0 |
| 1.55 | 1.3169E0 | 1.3493E0 | 1.3938E0 | 1.4525E0 | 1.5265E0 | 1.6132E0 | 1.7076E0 | 1.8116E0 | 1.9216E0 | 2.0479E0 | 2.1986E0 |
| 1.60 | 1.5506E0 | 1.5905E0 | 1.6423E0 | 1.7105E0 | 1.7982E0 | 1.9024E0 | 2.0192E0 | 2.1475E0 | 2.2859E0 | 2.4456E0 | 2.6350E0 |
| 1.65 | 1.8494E0 | 1.8876E0 | 1.9400E0 | 2.0176E0 | 2.1222E0 | 2.2487E0 | 2.3854E0 | 2.5297E0 | 2.6880E0 | 2.8851E0 | 3.1672E0 |
| 1.70 | 2.1868E0 | 2.2301E0 | 2.2891E0 | 2.3776E0 | 2.4987E0 | 2.6461E0 | 2.8063E0 | 2.9789E0 | 3.1757E0 | 3.4372E0 | 3.8086E0 |
| 1.75 | 2.5464E0 | 2.6066E0 | 2.6840E0 | 2.7871E0 | 2.9109E0 | 3.0605E0 | 3.2422E0 | 3.4611E0 | 3.7308E0 | 4.0964E0 | 4.5170E0 |
| 1.80 | 2.9278E0 | 3.0064E0 | 3.1132E0 | 3.2333E0 | 3.3655E0 | 3.5295E0 | 3.7607E0 | 4.0750E0 | 4.4834E0 | 4.9978E0 | 5.4955E0 |
| 1.85 | 3.3332E0 | 3.4363E0 | 3.5720E0 | 3.7195E0 | 3.8858E0 | 4.1114E0 | 4.4494E0 | 4.9275E0 | 5.5318E0 | 6.2190E0 | |
| 1.90 | 3.8614E0 | 3.9637E0 | 4.1114E0 | 4.2858E0 | 4.5065E0 | 4.8307E0 | 5.3017E0 | 5.9501E0 | |||
| 1.95 | 4.5113E0 | 4.6182E0 | 4.7604E0 | 4.9550E0 | 5.2460E0 | 5.6713E0 | 6.2825E0 | ||||
| 2.00 | 5.1900E0 | 5.3031E0 | 5.4286E0 | 5.6327E0 | 5.9711E0 | ||||||
| 2.05 | 5.9009E0 | 6.0686E0 | 6.1916E0 | ||||||||
| 2.10 | 6.6428E0 | 6.8086E0 | |||||||||
| Table 12. Ratio of specific heats (Cp/Cv) | |||||||||||
| Temp. | Pressure (atm) | ||||||||||
| (K) | .00 | 2.50 | 5.00 | 7.50 | 10.00 | 12.50 | 15.00 | 17.50 | 20.00 | 22.50 | 25.00 |
0.10 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
1.0000E0 |
| 0.15 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.20 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.25 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.30 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.35 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.40 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.45 | 1.0001E0 | 1.0001E0 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.50 | 1.0001E0 | 1.0001E0 | 1.0001E0 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.55 | 1.0002E0 | 1.0001E0 | 1.0001E0 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.60 | 1.0002E0 | 1.0002E0 | 1.0001E0 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.65 | 1.0003E0 | 1.0002E0 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 |
| 0.70 | 1.0003E0 | 1.0001E0 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0001E0 | 1.0001E0 |
| 0.75 | 1.0002E0 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0001E0 | 1.0001E0 | 1.0002E0 |
| 0.80 | 1.0002E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0001E0 | 1.0001E0 | 1.0002E0 | 1.0003E0 | 1.0004E0 |
| 0.85 | 1.0002E0 | 1.0000E0 | 1.0000E0 | 1.0000E0 | 1.0001E0 | 1.0001E0 | 1.0002E0 | 1.0003E0 | 1.0004E0 | 1.0005E0 | 1.0007E0 |
| 0.90 | 1.0001E0 | 1.0000E0 | 1.0000E0 | 1.0001E0 | 1.0002E0 | 1.0002E0 | 1.0003E0 | 1.0004E0 | 1.0006E0 | 1.0008E0 | 1.0011E0 |
| 0.95 | 1.0001E0 | 1.0000E0 | 1.0001E0 | 1.0003E0 | 1.0004E0 | 1.0004E0 | 1.0006E0 | 1.0007E0 | 1.0010E0 | 1.0013E0 | 1.0016E0 |
| 1.00 | 1.0001E0 | 1.0000E0 | 1.0002E0 | 1.0004E0 | 1.0006E0 | 1.0007E0 | 1.0008E0 | 1.0011E0 | 1.0014E0 | 1.0018E0 | 1.0023E0 |
| 1.05 | 1.0000E0 | 1.0001E0 | 1.0004E0 | 1.0006E0 | 1.0008E0 | 1.0010E0 | 1.0012E0 | 1.0016E0 | 1.0021E0 | 1.0024E0 | 1.0033E0 |
| 1.10 | 1.0000E0 | 1.0002E0 | 1.0005E0 | 1.0009E0 | 1.0012E0 | 1.0014E0 | 1.0018E0 | 1.0022E0 | 1.0028E0 | 1.0035E0 | 1.0044E0 |
| 1.15 | 1.0000E0 | 1.0002E0 | 1.0006E0 | 1.0011E0 | 1.0016E0 | 1.0020E0 | 1.0025E0 | 1.0030E0 | 1.0038E0 | 1.0045E0 | 1.0059E0 |
| 1.20 | 1.0000E0 | 1.0003E0 | 1.0008E0 | 1.0014E0 | 1.0020E0 | 1.0026E0 | 1.0033E0 | 1.0041E0 | 1.0050E0 | 1.0063E0 | 1.0079E0 |
| 1.25 | 1.0000E0 | 1.0004E0 | 1.0010E0 | 1.0015E0 | 1.0022E0 | 1.0030E0 | 1.0040E0 | 1.0054E0 | 1.0069E0 | 1.0083E0 | 1.0091E0 |
| 1.30 | 1.0001E0 | 1.0005E0 | 1.0011E0 | 1.0020E0 | 1.0029E0 | 1.0039E0 | 1.0051E0 | 1.0065E0 | 1.0085E0 | 1.0107E0 | 1.0143E0 |
| 1.35 | 1.0001E0 | 1.0007E0 | 1.0015E0 | 1.0024E0 | 1.0035E0 | 1.0046E0 | 1.0062E0 | 1.0080E0 | 1.0103E0 | 1.0129E0 | 1.0155E0 |
| 1.40 | 1.0002E0 | 1.0009E0 | 1.0019E0 | 1.0031E0 | 1.0044E0 | 1.0059E0 | 1.0078E0 | 1.0099E0 | 1.0126E0 | 1.0157E0 | 1.0189E0 |
| 1.45 | 1.0003E0 | 1.0011E0 | 1.0024E0 | 1.0038E0 | 1.0055E0 | 1.0075E0 | 1.0099E0 | 1.0130E0 | 1.0170E0 | 1.0208E0 | 1.0268E0 |
| 1.00 | 1.0004E0 | 1.0014E0 | 1.0029E0 | 1.0047E0 | 1.0069E0 | 1.0095E0 | 1.0124E0 | 1.0164E0 | 1.0217E0 | 1.0277E0 | 1.0361E0 |
| 1.55 | 1.0006E0 | 1.0017E0 | 1.0036E0 | 1.0060E0 | 1.0087E0 | 1.0117E0 | 1.0151E0 | 1.0193E0 | 1.0250E0 | 1.0328E0 | 1.0454E0 |
| 1.60 | 1.0007E0 | 1.0020E0 | 1.0042E0 | 1.0073E0 | 1.0108E0 | 1.0145E0 | 1.0186E0 | 1.0234E0 | 1.0305E0 | 1.0402E0 | 1.0583E0 |
| 1.65 | 1.0008E0 | 1.0025E0 | 1.0051E0 | 1.0087E0 | 1.0133E0 | 1.0181E0 | 1.0234E0 | 1.0299E0 | 1.0387E0 | 1.0504E0 | 1.0672E0 |
| 1.70 | 1.0011E0 | 1.0028E0 | 1.0059E0 | 1.0105E0 | 1.0162E0 | 1.0224E0 | 1.0290E0 | 1.0370E0 | 1.0490E0 | 1.0656E0 | 1.0958E0 |
| 1.75 | 1.0011E0 | 1.0026E0 | 1.0064E0 | 1.0127E0 | 1.0205E0 | 1.0277E0 | 1.0340E0 | 1.0415E0 | 1.0559E0 | 1.0798E0 | 1.1382E0 |
| 1.80 | 1.0014E0 | 1.0034E0 | 1.0077E0 | 1.0149E0 | 1.0245E0 | 1.0342E0 | 1.0431E0 | 1.0548E0 | 1.0772E0 | 1.1137E0 | 1.1935E0 |
| 1.85 | 1.0019E0 | 1.0044E0 | 1.0099E0 | 1.0171E0 | 1.0259E0 | 1.0369E0 | 1.0508E0 | 1.0699E0 | 1.1052E0 | 1.1617E0 | |
| 1.90 | 1.0020E0 | 1.0061E0 | 1.0121E0 | 1.0203E0 | 1.0314E0 | 1.0477E0 | 1.0715E0 | 1.1060E0 | |||
| 1.95 | 1.0024E0 | 1.0071E0 | 1.0145E0 | 1.0245E0 | 1.0407E0 | 1.0678E0 | 1.1074E0 | ||||
| 2.00 | 1.0026E0 | 1.0081E0 | 1.0169E0 | 1.0308E0 | 1.0556E0 | ||||||
| 2.05 | 1.0036E0 | 1.0096E0 | 1.0191E0 | ||||||||
| 2.10 | 1.0051E0 | 1.0099E0 | |||||||||
| Table 13. Phonon number density (cm-3) | |||||||||||
| Temp. | Pressure (atm) | ||||||||||
| (K) | .00 | 2.50 | 5.00 | 7.50 | 10.00 | 12.50 | 15.00 | 17.50 | 20.00 | 22.50 | 25.00 |
0.10 |
2.0148E16 |
1.5987E16 |
1.3244E16 |
1.1301E16 |
9.8534E15 |
8.7335E15 |
7.8416E15 |
7.1146E15 |
6.5106E15 |
6.0010E15 |
5.5652E15 |
| 0.15 | 6.7739E16 | 5.3861E16 | 4.4667E16 | 3.8138E16 | 3.3264E16 | 2.9490E16 | 2.6483E16 | 2.4030E16 | 2.1992E16 | 2.0271E16 | 1.8800E16 |
| 0.20 | 1.5979E17 | 1.2738E17 | 1.0579E17 | 9.0395E16 | 7.8882E16 | 6.9953E16 | 6.2831E16 | 5.7019E16 | 5.2188E16 | 4.8108E16 | 4.4618E16 |
| 0.25 | 3.1034E17 | 2.4815E17 | 2.0642E17 | 1.7656E17 | 1.5416E17 | 1.3676E17 | 1.2287E17 | 1.1152E17 | 1.0208E17 | 9.4110E16 | 8.7288E16 |
| 0.30 | 5.3296E17 | 4.2760E17 | 3.5636E17 | 3.0513E17 | 2.6660E17 | 2.3661E17 | 2.1263E17 | 1.9304E17 | 1.7672E17 | 1.6294E17 | 1.5114E17 |
| 0.35 | 8.4081E17 | 6.7700E17 | |||||||||