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 21. Energy of maxon peak (K) | |||||||||||
| 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 |
1.3816E1 |
1.4197E1 |
1.4438E1 |
1.4592E1 |
1.4691E1 |
1.4752E1 |
1.4789E1 |
1.4809E1 |
1.4819E1 |
1.4822E1 |
1.4822E1 |
| 0.15 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.20 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.25 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.30 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.35 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.40 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.45 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.50 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.55 | 1.3816E1 | 1.4197E1 | 1.4438E1 | 1.4592E1 | 1.4691E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4822E1 |
| 0.60 | 1.3816E1 | 1.4197E1 | 1.4437E1 | 1.4592E1 | 1.4690E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4819E1 | 1.4822E1 | 1.4821E1 |
| 0.65 | 1.3816E1 | 1.4196E1 | 1.4437E1 | 1.4592E1 | 1.4690E1 | 1.4752E1 | 1.4789E1 | 1.4809E1 | 1.4818E1 | 1.4822E1 | 1.4821E1 |
| 0.70 | 1.3815E1 | 1.4196E1 | 1.4437E1 | 1.4592E1 | 1.4690E1 | 1.4752E1 | 1.4788E1 | 1.4809E1 | 1.4818E1 | 1.4821E1 | 1.4821E1 |
| 0.75 | 1.3815E1 | 1.4196E1 | 1.4437E1 | 1.4591E1 | 1.4690E1 | 1.4751E1 | 1.4788E1 | 1.4808E1 | 1.4818E1 | 1.4821E1 | 1.4821E1 |
| 0.80 | 1.3815E1 | 1.4195E1 | 1.4436E1 | 1.4591E1 | 1.4689E1 | 1.4751E1 | 1.4787E1 | 1.4808E1 | 1.4817E1 | 1.4821E1 | 1.4820E1 |
| 0.85 | 1.3814E1 | 1.4195E1 | 1.4436E1 | 1.4590E1 | 1.4689E1 | 1.4750E1 | 1.4787E1 | 1.4807E1 | 1.4817E1 | 1.4820E1 | 1.4820E1 |
| 0.90 | 1.3813E1 | 1.4194E1 | 1.4434E1 | 1.4589E1 | 1.4687E1 | 1.4749E1 | 1.4786E1 | 1.4806E1 | 1.4816E1 | 1.4819E1 | 1.4818E1 |
| 0.95 | 1.3812E1 | 1.4192E1 | 1.4433E1 | 1.4587E1 | 1.4686E1 | 1.4748E1 | 1.4784E1 | 1.4804E1 | 1.4814E1 | 1.4817E1 | 1.4817E1 |
| 1.00 | 1.3810E1 | 1.4190E1 | 1.4431E1 | 1.4585E1 | 1.4684E1 | 1.4745E1 | 1.4782E1 | 1.4802E1 | 1.4812E1 | 1.4815E1 | 1.4815E1 |
| 1.05 | 1.3807E1 | 1.4188E1 | 1.4428E1 | 1.4583E1 | 1.4681E1 | 1.4743E1 | 1.4779E1 | 1.4800E1 | 1.4809E1 | 1.4812E1 | 1.4812E1 |
| 1.10 | 1.3804E1 | 1.4184E1 | 1.4425E1 | 1.4579E1 | 1.4678E1 | 1.4739E1 | 1.4776E1 | 1.4796E1 | 1.4806E1 | 1.4809E1 | 1.4809E1 |
| 1.15 | 1.3799E1 | 1.4180E1 | 1.4420E1 | 1.4575E1 | 1.4673E1 | 1.4734E1 | 1.4771E1 | 1.4791E1 | 1.4801E1 | 1.4804E1 | 1.4804E1 |
| 1.20 | 1.3796E1 | 1.4174E1 | 1.4414E1 | 1.4568E1 | 1.4667E1 | 1.4728E1 | 1.4765E1 | 1.4785E1 | 1.4795E1 | 1.4798E1 | 1.4798E1 |
| 1.25 | 1.3786E1 | 1.4166E1 | 1.4406E1 | 1.4561E1 | 1.4659E1 | 1.4720E1 | 1.4757E1 | 1.4777E1 | 1.4787E1 | 1.4790E1 | 1.4790E1 |
| 1.30 | 1.3777E1 | 1.4156E1 | 1.4397E1 | 1.4551E1 | 1.4649E1 | 1.4710E1 | 1.4747E1 | 1.4767E1 | 1.4777E1 | 1.4780E1 | 1.4780E1 |
| 1.35 | 1.3765E1 | 1.4144E1 | 1.4384E1 | 1.4538E1 | 1.4636E1 | 1.4698E1 | 1.4734E1 | 1.4754E1 | 1.4764E1 | 1.4767E1 | 1.4767E1 |
| 1.40 | 1.3750E1 | 1.4129E1 | 1.4369E1 | 1.4523E1 | 1.4621E1 | 1.4682E1 | 1.4718E1 | 1.4739E1 | 1.4748E1 | 1.4751E1 | 1.4751E1 |
| 1.45 | 1.3732E1 | 1.4110E1 | 1.4350E1 | 1.4503E1 | 1.4601E1 | 1.4662E1 | 1.4699E1 | 1.4719E1 | 1.4728E1 | 1.4732E1 | 1.4731E1 |
| 1.50 | 1.3709E1 | 1.4087E1 | 1.4326E1 | 1.4479E1 | 1.4577E1 | 1.4638E1 | 1.4675E1 | 1.4695E1 | 1.4704E1 | 1.4707E1 | 1.4707E1 |
| 1.55 | 1.3682E1 | 1.4059E1 | 1.4297E1 | 1.4450E1 | 1.4548E1 | 1.4609E1 | 1.4645E1 | 1.4665E1 | 1.4675E1 | 1.4678E1 | 1.4678E1 |
| 1.60 | 1.3648E1 | 1.4024E1 | 1.4262E1 | 1.4415E1 | 1.4512E1 | 1.4573E1 | 1.4609E1 | 1.4629E1 | 1.4639E1 | 1.4642E1 | 1.4642E1 |
| 1.65 | 1.3608E1 | 1.3983E1 | 1.4220E1 | 1.4372E1 | 1.4469E1 | 1.4530E1 | 1.4566E1 | 1.4586E1 | 1.4596E1 | 1.4599E1 | 1.4599E1 |
| 1.70 | 1.3560E1 | 1.3933E1 | 1.4170E1 | 1.4321E1 | 1.4418E1 | 1.4478E1 | 1.4514E1 | 1.4534E1 | 1.4544E1 | 1.4547E1 | 1.4547E1 |
| 1.75 | 1.3502E1 | 1.3874E1 | 1.4109E1 | 1.4260E1 | 1.4357E1 | 1.4417E1 | 1.4453E1 | 1.4473E1 | 1.4482E1 | 1.4485E1 | 1.4485E1 |
| 1.80 | 1.3433E1 | 1.3804E1 | 1.4038E1 | 1.4188E1 | 1.4284E1 | 1.4344E1 | 1.4379E1 | 1.4399E1 | 1.4409E1 | 1.4412E1 | 1.4411E1 |
| 1.85 | 1.3353E1 | 1.3721E1 | 1.3953E1 | 1.4103E1 | 1.4198E1 | 1.4257E1 | 1.4293E1 | 1.4313E1 | 1.4322E1 | 1.4325E1 | |
| 1.90 | 1.3258E1 | 1.3623E1 | 1.3854E1 | 1.4002E1 | 1.4097E1 | 1.4156E1 | 1.4191E1 | 1.4211E1 | |||
| 1.95 | 1.3146E1 | 1.3508E1 | 1.3738E1 | 1.3885E1 | 1.3978E1 | 1.4037E1 | 1.4072E1 | ||||
| 2.00 | 1.3016E1 | 1.3375E1 | 1.3602E1 | 1.3748E1 | 1.3840E1 | ||||||
| 2.05 | 1.2865E1 | 1.3220E1 | 1.3444E1 | ||||||||
| 2.10 | 1.2691E1 | 1.3041E1 | |||||||||
| Table 22. Thermal roton energy gap (K) | |||||||||||
| 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 |
8.7117E0 |
8.5726E0 |
8.3799E0 |
8.1893E0 |
8.0193E0 |
7.8676E0 |
7.7323E0 |
7.6020E0 |
7.4729E0 |
7.3429E0 |
7.2102E0 |
| 0.15 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.20 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.25 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.30 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.35 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.40 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.45 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.50 | 8.7117E0 | 8.5726E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2102E0 |
| 0.55 | 8.7117E0 | 8.5725E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2101E0 |
| 0.60 | 8.7116E0 | 8.5725E0 | 8.3799E0 | 8.1893E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3429E0 | 7.2101E0 |
| 0.65 | 8.7114E0 | 8.5723E0 | 8.3798E0 | 8.1892E0 | 8.0193E0 | 7.8676E0 | 7.7323E0 | 7.6020E0 | 7.4729E0 | 7.3428E0 | 7.2101E0 |
| 0.70 | 8.7109E0 | 8.5718E0 | 8.3795E0 | 8.1891E0 | 8.0192E0 | 7.8676E0 | 7.7323E0 | 7.6019E0 | 7.4728E0 | 7.3428E0 | 7.2100E0 |
| 0.75 | 8.7098E0 | 8.5708E0 | 8.3789E0 | 8.1889E0 | 8.0192E0 | 7.8676E0 | 7.7323E0 | 7.6019E0 | 7.4727E0 | 7.3426E0 | 7.2099E0 |
| 0.80 | 8.7077E0 | 8.5689E0 | 8.3777E0 | 8.1884E0 | 8.0190E0 | 7.8676E0 | 7.7322E0 | 7.6018E0 | 7.4725E0 | 7.3424E0 | 7.2096E0 |
| 0.85 | 8.7039E0 | 8.5653E0 | 8.3757E0 | 8.1875E0 | 8.0188E0 | 7.8677E0 | 7.7321E0 | 7.6016E0 | 7.4721E0 | 7.3419E0 | 7.2091E0 |
| 0.90 | 8.6976E0 | 8.5595E0 | 8.3722E0 | 8.1861E0 | 8.0184E0 | 7.8677E0 | 7.7319E0 | 7.6012E0 | 7.4715E0 | 7.3412E0 | 7.2083E0 |
| 0.95 | 8.6877E0 | 8.5503E0 | 8.3667E0 | 8.1838E0 | 8.0177E0 | 7.8678E0 | 7.7316E0 | 7.6007E0 | 7.4705E0 | 7.3400E0 | 7.2070E0 |
| 1.00 | 8.6729E0 | 8.5366E0 | 8.3586E0 | 8.1804E0 | 8.0168E0 | 7.8680E0 | 7.7312E0 | 7.5999E0 | 7.4691E0 | 7.3382E0 | 7.2051E0 |
| 1.05 | 8.6494E0 | 8.5148E0 | 8.3457E0 | 8.1751E0 | 8.0154E0 | 7.8685E0 | 7.7308E0 | 7.5991E0 | 7.4672E0 | 7.3361E0 | 7.2030E0 |
| 1.10 | 8.6218E0 | 8.4893E0 | 8.3305E0 | 8.1686E0 | 8.0135E0 | 7.8686E0 | 7.7298E0 | 7.5973E0 | 7.4640E0 | 7.3321E0 | 7.1985E0 |
| 1.15 | 8.5950E0 | 8.4673E0 | 8.3186E0 | 8.1647E0 | 8.0131E0 | 7.8673E0 | 7.7284E0 | 7.5912E0 | 7.4586E0 | 7.3243E0 | 7.1891E0 |
| 1.20 | 8.5738E0 | 8.4464E0 | 8.3030E0 | 8.1557E0 | 8.0075E0 | 7.8641E0 | 7.7232E0 | 7.5860E0 | 7.4502E0 | 7.3123E0 | 7.1722E0 |
| 1.25 | 8.5557E0 | 8.4234E0 | 8.2823E0 | 8.1392E0 | 8.0009E0 | 7.8640E0 | 7.7262E0 | 7.5868E0 | 7.4437E0 | 7.3020E0 | 7.1634E0 |
| 1.30 | 8.5370E0 | 8.4088E0 | 8.2719E0 | 8.1310E0 | 7.9892E0 | 7.8476E0 | 7.7065E0 | 7.5661E0 | 7.4221E0 | 7.2771E0 | 7.1241E0 |
| 1.35 | 8.5255E0 | 8.3901E0 | 8.2482E0 | 8.1056E0 | 7.9646E0 | 7.8242E0 | 7.6835E0 | 7.5385E0 | 7.3944E0 | 7.2441E0 | 7.0942E0 |
| 1.40 | 8.4966E0 | 8.3598E0 | 8.2167E0 | 8.0719E0 | 7.9279E0 | 7.7845E0 | 7.6391E0 | 7.4925E0 | 7.3454E0 | 7.1929E0 | 7.0399E0 |
| 1.45 | 8.4504E0 | 8.3111E0 | 8.1684E0 | 8.0243E0 | 7.8790E0 | 7.7330E0 | 7.5848E0 | 7.4337E0 | 7.2785E0 | 7.1182E0 | 6.9550E0 |
| 1.50 | 8.4160E0 | 8.2737E0 | 8.1307E0 | 7.9832E0 | 7.8365E0 | 7.6867E0 | 7.5333E0 | 7.3777E0 | 7.2175E0 | 7.0513E0 | 6.8762E0 |
| 1.55 | 8.3956E0 | 8.2501E0 | 8.1035E0 | 7.9541E0 | 7.8005E0 | 7.6457E0 | 7.4887E0 | 7.3306E0 | 7.1677E0 | 6.9982E0 | 6.8140E0 |
| 1.60 | 8.3759E0 | 8.2274E0 | 8.0782E0 | 7.9235E0 | 7.7641E0 | 7.6020E0 | 7.4387E0 | 7.2725E0 | 7.1025E0 | 6.9240E0 | 6.7276E0 |
| 1.65 | 8.3428E0 | 8.1909E0 | 8.0370E0 | 7.8778E0 | 7.7126E0 | 7.5419E0 | 7.3699E0 | 7.1922E0 | 7.0129E0 | 6.8244E0 | 6.6191E0 |
| 1.70 | 8.2894E0 | 8.1317E0 | 7.9752E0 | 7.8114E0 | 7.6384E0 | 7.4616E0 | 7.2799E0 | 7.0952E0 | 6.9050E0 | 6.6995E0 | 6.4689E0 |
| 1.75 | 8.2227E0 | 8.0682E0 | 7.9131E0 | 7.7439E0 | 7.5630E0 | 7.3744E0 | 7.1877E0 | 6.9996E0 | 6.8051E0 | 6.5885E0 | 6.3261E0 |
| 1.80 | 8.1594E0 | 7.9973E0 | 7.8352E0 | 7.6617E0 | 7.4730E0 | 7.2769E0 | 7.0777E0 | 6.8746E0 | 6.6589E0 | 6.4105E0 | 6.1073E0 |
| 1.85 | 8.0920E0 | 7.9210E0 | 7.7472E0 | 7.5648E0 | 7.3766E0 | 7.1792E0 | 6.9765E0 | 6.7559E0 | 6.5108E0 | 6.2240E0 | |
| 1.90 | 8.0215E0 | 7.8419E0 | 7.6574E0 | 7.4669E0 | 7.2696E0 | 7.0607E0 | 6.8320E0 | 6.5780E0 | |||
| 1.95 | 7.9480E0 | 7.7614E0 | 7.5687E0 | 7.3688E0 | 7.1573E0 | 6.9217E0 | 6.6558E0 | ||||
| 2.00 | 7.8425E0 | 7.6502E0 | 7.4512E0 | 7.2422E0 | 7.0120E0 | ||||||
| 2.05 | 7.7268E0 | 7.5260E0 | 7.3215E0 | ||||||||
| 2.10 | 7.6284E0 | 7.4221E0 | |||||||||
| Table 23. Thermal roton effective mass (m) | |||||||||||
| 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 |
1.6079E-1 |
1.5803E-1 |
1.5432E-1 |
1.5066E-1 |
1.4739E-1 |
1.4447E-1 |
1.4186E-1 |
1.3935E-1 |
1.3687E-1 |
1.3438E-1 |
1.3185E-1 |
| 0.15 | 1.6079E-1 | 1.5803E-1 | 1.5432E-1 | 1.5066E-1 | 1.4739E-1 | 1.4447E-1 | 1.4186E-1 | 1.3935E-1 | 1.3687E-1 | 1.3438E-1 | 1.3185E-1 |
| 0.20 | 1.6079E-1 | 1.5803E-1 | 1.5432E-1 | 1.5066E-1 | 1.4739E-1 | 1.4447E-1 | 1.4186E-1 | 1.3935E-1 | 1.3687E-1 | 1.3438E-1 | 1.3185E-1 |
| 0.25 | 1.6079E-1 | 1.5803E-1 | 1.5432E-1 | 1.5066E-1 | 1.4739E-1 | 1.4447E-1 | 1.4186E-1 | 1.3935E-1 | 1.3687E-1 | 1.3438E-1 | 1.3185E-1 |
| 0.30 | 1.6079E-1 | 1.5803E-1 | 1.5432E-1 | 1.5066E-1 | 1.4739E-1 | 1.4447E-1 | 1.4186E-1 | 1.3935E-1 | 1.3687E-1 | 1.3438E-1 | 1.3185E-1 |
| 0.35 | 1.6079E-1 | 1.5803E-1 | 1.5432E-1 | 1.5066E-1 | |||||||