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 6. Helmholtz free energy of excitations (J g-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 |
-1.395E-6 |
-1.079E-6 |
-8.744E-7 |
-7.314E-7 |
-6.264E-7 |
-5.463E-7 |
-4.832E-7 |
-4.324E-7 |
-3.907E-7 |
-3.558E-7 |
-3.263E-7 |
| 0.15 | -2.092E-6 | -1.619E-6 | -1.312E-6 | -1.097E-6 | -9.396E-7 | -8.194E-7 | -7.248E-7 | -6.486E-7 | -5.860E-7 | -5.337E-7 | -4.894E-7 |
| 0.20 | -3.957E-6 | -3.067E-6 | -2.487E-6 | -2.082E-6 | -1.784E-6 | -1.556E-6 | -1.376E-6 | -1.232E-6 | -1.113E-6 | -1.014E-6 | -9.295E-7 |
| 0.25 | -7.859E-6 | -6.110E-6 | -4.963E-6 | -4.158E-6 | -3.564E-6 | -3.110E-6 | -2.752E-6 | -2.464E-6 | -2.226E-6 | -2.028E-6 | -1.860E-6 |
| 0.30 | -1.489E-5 | -1.162E-5 | -9.460E-6 | -7.935E-6 | -6.807E-6 | -5.942E-6 | -5.260E-6 | -4.709E-6 | -4.256E-6 | -3.877E-6 | -3.556E-6 |
| 0.35 | -2.637E-5 | -2.066E-5 | -1.686E-5 | -1.416E-5 | -1.216E-5 | -1.062E-5 | -9.402E-6 | -8.420E-6 | -7.611E-6 | -6.935E-6 | -6.361E-6 |
| 0.40 | -4.382E-5 | -3.447E-5 | -2.819E-5 | -2.371E-5 | -2.038E-5 | -1.781E-5 | -1.578E-5 | -1.414E-5 | -1.279E-5 | -1.165E-5 | -1.070E-5 |
| 0.45 | -6.897E-5 | -5.449E-5 | -4.468E-5 | -3.765E-5 | -3.239E-5 | -2.834E-5 | -2.513E-5 | -2.254E-5 | -2.041E-5 | -1.864E-5 | -1.714E-5 |
| 0.50 | -1.038E-4 | -8.236E-5 | -6.774E-5 | -5.721E-5 | -4.933E-5 | -4.325E-5 | -3.845E-5 | -3.459E-5 | -3.144E-5 | -2.885E-5 | -2.671E-5 |
| 0.55 | -1.505E-4 | -1.201E-4 | -9.915E-5 | -8.407E-5 | -7.279E-5 | -6.413E-5 | -5.733E-5 | -5.194E-5 | -4.763E-5 | -4.421E-5 | -4.156E-5 |
| 0.60 | -2.120E-4 | -1.702E-4 | -1.414E-4 | -1.207E-4 | -1.054E-4 | -9.372E-5 | -8.473E-5 | -7.780E-5 | -7.256E-5 | -6.873E-5 | -6.627E-5 |
| 0.65 | -2.922E-4 | -2.365E-4 | -1.984E-4 | -1.714E-4 | -1.517E-4 | -1.371E-4 | -1.262E-4 | -1.184E-4 | -1.132E-4 | -1.103E-4 | -1.098E-4 |
| 0.70 | -3.967E-4 | -3.249E-4 | -2.766E-4 | -2.431E-4 | -2.196E-4 | -2.030E-4 | -1.917E-4 | -1.847E-4 | -1.818E-4 | -1.828E-4 | -1.880E-4 |
| 0.75 | -5.345E-4 | -4.446E-4 | -3.860E-4 | -3.475E-4 | -3.221E-4 | -3.063E-4 | -2.974E-4 | -2.950E-4 | -2.987E-4 | -3.089E-4 | -3.263E-4 |
| 0.80 | -7.188E-4 | -6.098E-4 | -5.429E-4 | -5.027E-4 | -4.797E-4 | -4.695E-4 | -4.683E-4 | -4.767E-4 | -4.942E-4 | -5.226E-4 | -5.618E-4 |
| 0.85 | -9.697E-4 | -8.414E-4 | -7.706E-4 | -7.350E-4 | -7.218E-4 | -7.253E-4 | -7.406E-4 | -7.694E-4 | -8.117E-4 | -8.703E-4 | -9.461E-4 |
| 0.90 | -1.315E-3 | -1.170E-3 | -1.102E-3 | -1.081E-3 | -1.090E-3 | -1.118E-3 | -1.162E-3 | -1.225E-3 | -1.308E-3 | -1.415E-3 | -1.548E-3 |
| 0.95 | -1.793E-3 | -1.636E-3 | -1.583E-3 | -1.591E-3 | -1.635E-3 | -1.707E-3 | -1.797E-3 | -1.912E-3 | -2.055E-3 | -2.235E-3 | -2.449E-3 |
| 1.00 | -2.458E-3 | -2.294E-3 | -2.270E-3 | -2.325E-3 | -2.428E-3 | -2.561E-3 | -2.720E-3 | -2.912E-3 | -3.144E-3 | -3.425E-3 | -3.755E-3 |
| 1.05 | -3.375E-3 | -3.216E-3 | -3.238E-3 | -3.364E-3 | -3.549E-3 | -3.771E-3 | -4.028E-3 | -4.326E-3 | -4.679E-3 | -5.098E-3 | -5.584E-3 |
| 1.10 | -4.634E-3 | -4.491E-3 | -4.579E-3 | -4.798E-3 | -5.093E-3 | -5.436E-3 | -5.825E-3 | -6.266E-3 | -6.784E-3 | -7.384E-3 | -8.076E-3 |
| 1.15 | -6.335E-3 | -6.224E-3 | -6.398E-3 | -6.736E-3 | -7.176E-3 | -7.678E-3 | -8.241E-3 | -8.873E-3 | -9.595E-3 | -1.043E-2 | -1.139E-2 |
| 1.20 | -8.599E-3 | -8.535E-3 | -8.813E-3 | -9.301E-3 | -9.922E-3 | -1.063E-2 | -1.141E-2 | -1.229E-2 | -1.328E-2 | -1.442E-2 | -1.570E-2 |
| 1.25 | -1.155E-2 | -1.156E-2 | -1.198E-2 | -1.265E-2 | -1.349E-2 | -1.443E-2 | -1.550E-2 | -1.668E-2 | -1.801E-2 | -1.953E-2 | -2.122E-2 |
| 1.30 | -1.534E-2 | -1.545E-2 | -1.604E-2 | -1.693E-2 | -1.802E-2 | -1.927E-2 | -2.066E-2 | -2.221E-2 | -2.397E-2 | -2.597E-2 | -2.817E-2 |
| 1.35 | -2.013E-2 | -2.037E-2 | -2.116E-2 | -2.232E-2 | -2.374E-2 | -2.536E-2 | -2.716E-2 | -2.918E-2 | -3.144E-2 | -3.401E-2 | -3.689E-2 |
| 1.40 | -2.610E-2 | -2.651E-2 | -2.758E-2 | -2.908E-2 | -3.088E-2 | -3.294E-2 | -3.523E-2 | -3.779E-2 | -4.068E-2 | -4.395E-2 | -4.756E-2 |
| 1.45 | -3.353E-2 | -3.415E-2 | -3.553E-2 | -3.745E-2 | -3.972E-2 | -4.232E-2 | -4.523E-2 | -4.848E-2 | -5.211E-2 | -5.622E-2 | -6.081E-2 |
| 1.50 | -4.265E-2 | -4.355E-2 | -4.534E-2 | -4.772E-2 | -5.056E-2 | -5.379E-2 | -5.742E-2 | -6.148E-2 | -6.606E-2 | -7.122E-2 | -7.697E-2 |
| 1.55 | -5.364E-2 | -5.488E-2 | -5.711E-2 | -6.006E-2 | -6.359E-2 | -6.760E-2 | -7.212E-2 | -7.715E-2 | -8.280E-2 | -8.919E-2 | -9.642E-2 |
| 1.60 | -6.674E-2 | -6.836E-2 | -7.113E-2 | -7.476E-2 | -7.910E-2 | -8.404E-2 | -8.954E-2 | -9.570E-2 | -1.027E-1 | -1.105E-1 | -1.194E-1 |
| 1.65 | -8.220E-2 | -8.427E-2 | -8.765E-2 | -9.208E-2 | -9.740E-2 | -1.035E-1 | -1.102E-1 | -1.177E-1 | -1.262E-1 | -1.358E-1 | -1.469E-1 |
| 1.70 | -1.005E-1 | -1.030E-1 | -1.072E-1 | -1.126E-1 | -1.190E-1 | -1.264E-1 | -1.346E-1 | -1.438E-1 | -1.541E-1 | -1.659E-1 | -1.795E-1 |
| 1.75 | -1.219E-1 | -1.251E-1 | -1.301E-1 | -1.366E-1 | -1.444E-1 | -1.533E-1 | -1.633E-1 | -1.745E-1 | -1.870E-1 | -2.014E-1 | -2.184E-1 |
| 1.80 | -1.471E-1 | -1.509E-1 | -1.568E-1 | -1.646E-1 | -1.740E-1 | -1.849E-1 | -1.969E-1 | -2.103E-1 | -2.254E-1 | -2.430E-1 | -2.643E-1 |
| 1.85 | -1.762E-1 | -1.810E-1 | -1.880E-1 | -1.973E-1 | -2.086E-1 | -2.216E-1 | -2.361E-1 | -2.523E-1 | -2.708E-1 | -2.927E-1 | |
| 1.90 | -2.100E-1 | -2.157E-1 | -2.241E-1 | -2.353E-1 | -2.486E-1 | -2.640E-1 | -2.814E-1 | -3.010E-1 | |||
| 1.95 | -2.486E-1 | -2.557E-1 | -2.657E-1 | -2.789E-1 | -2.948E-1 | -3.133E-1 | -3.346E-1 | ||||
| 2.00 | -2.930E-1 | -3.015E-1 | -3.134E-1 | -3.291E-1 | -3.479E-1 | ||||||
| 2.05 | -3.440E-1 | -3.542E-1 | -3.684E-1 | ||||||||
| 2.10 | -4.023E-1 | -4.145E-1 | |||||||||
| Table 7. Gibbs free energy of excitations (J g-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 |
-1.395E-6 |
-1.079E-6 |
-8.744E-7 |
-7.314E-7 |
-6.264E-7 |
-5.463E-7 |
-4.832E-7 |
-4.324E-7 |
-3.907E-7 |
-3.558E-7 |
-3.263E-7 |
| 0.15 | -2.092E-6 | -1.619E-6 | -1.312E-6 | -1.097E-6 | -9.396E-7 | -8.194E-7 | -7.248E-7 | -6.486E-7 | -5.860E-7 | -5.337E-7 | -4.894E-7 |
| 0.20 | -3.957E-6 | -3.067E-6 | -2.487E-6 | -2.082E-6 | -1.784E-6 | -1.556E-6 | -1.376E-6 | -1.232E-6 | -1.113E-6 | -1.014E-6 | -9.295E-7 |
| 0.25 | -7.859E-6 | -6.110E-6 | -4.963E-6 | -4.158E-6 | -3.564E-6 | -3.110E-6 | -2.752E-6 | -2.464E-6 | -2.226E-6 | -2.028E-6 | -1.860E-6 |
| 0.30 | -1.489E-5 | -1.162E-5 | -9.460E-6 | -7.935E-6 | -6.807E-6 | -5.942E-6 | -5.260E-6 | -4.709E-6 | -4.256E-6 | -3.877E-6 | -3.556E-6 |
| 0.35 | -2.637E-5 | -2.066E-5 | -1.686E-5 | -1.416E-5 | -1.216E-5 | -1.062E-5 | -9.402E-6 | -8.420E-6 | -7.611E-6 | -6.935E-6 | -6.361E-6 |
| 0.40 | -4.382E-5 | -3.448E-5 | -2.819E-5 | -2.372E-5 | -2.038E-5 | -1.781E-5 | -1.578E-5 | -1.414E-5 | -1.279E-5 | -1.165E-5 | -1.070E-5 |
| 0.45 | -6.897E-5 | -5.449E-5 | -4.468E-5 | -3.765E-5 | -3.239E-5 | -2.834E-5 | -2.513E-5 | -2.254E-5 | -2.041E-5 | -1.864E-5 | -1.714E-5 |
| 0.50 | -1.038E-4 | -8.237E-5 | -6.774E-5 | -5.721E-5 | -4.933E-5 | -4.325E-5 | -3.845E-5 | -3.459E-5 | -3.144E-5 | -2.885E-5 | -2.671E-5 |
| 0.55 | -1.505E-4 | -1.201E-4 | -9.916E-5 | -8.407E-5 | -7.279E-5 | -6.413E-5 | -5.734E-5 | -5.194E-5 | -4.763E-5 | -4.421E-5 | -4.156E-5 |
| 0.60 | -2.120E-4 | -1.702E-4 | -1.414E-4 | -1.207E-4 | -1.054E-4 | -9.373E-5 | -8.474E-5 | -7.781E-5 | -7.256E-5 | -6.873E-5 | -6.627E-5 |
| 0.65 | -2.922E-4 | -2.366E-4 | -1.985E-4 | -1.714E-4 | -1.517E-4 | -1.371E-4 | -1.262E-4 | -1.184E-4 | -1.132E-4 | -1.103E-4 | -1.098E-4 |
| 0.70 | -3.968E-4 | -3.249E-4 | -2.766E-4 | -2.431E-4 | -2.196E-4 | -2.031E-4 | -1.917E-4 | -1.847E-4 | -1.818E-4 | -1.829E-4 | -1.880E-4 |
| 0.75 | -5.345E-4 | -4.446E-4 | -3.861E-4 | -3.475E-4 | -3.222E-4 | -3.064E-4 | -2.974E-4 | -2.950E-4 | -2.987E-4 | -3.089E-4 | -3.263E-4 |
| 0.80 | -7.188E-4 | -6.099E-4 | -5.429E-4 | -5.028E-4 | -4.797E-4 | -4.696E-4 | -4.683E-4 | -4.767E-4 | -4.942E-4 | -5.226E-4 | -5.617E-4 |
| 0.85 | -9.698E-4 | -8.415E-4 | -7.707E-4 | -7.351E-4 | -7.219E-4 | -7.254E-4 | -7.406E-4 | -7.694E-4 | -8.117E-4 | -8.702E-4 | -9.460E-4 |
| 0.90 | -1.315E-3 | -1.730E-3 | -1.103E-3 | -1.081E-3 | -1.090E-3 | -1.118E-3 | -1.162E-3 | -1.224E-3 | -1.307E-3 | -1.414E-3 | -1.547E-3 |
| 0.95 | -1.793E-3 | -1.636E-3 | -1.583E-3 | -1.591E-3 | -1.635E-3 | -1.706E-3 | -1.796E-3 | -1.911E-3 | -2.055E-3 | -2.340E-3 | -2.448E-3 |
| 1.00 | -2.458E-3 | -2.295E-3 | -2.270E-3 | -2.325E-3 | -2.428E-3 | -2.561E-3 | -2.719E-3 | -2.911E-3 | -3.143E-3 | -3.424E-3 | -3.753E-3 |
| 1.05 | -3.376E-3 | -3.217E-3 | -3.238E-3 | -3.364E-3 | -3.548E-3 | -3.770E-3 | -4.027E-3 | -4.325E-3 | -4.677E-3 | -5.095E-3 | -5.580E-3 |
| 1.10 | -4.634E-3 | -4.491E-3 | -4.579E-3 | -4.797E-3 | -5.092E-3 | -5.434E-3 | -5.823E-3 | -6.263E-3 | -6.780E-3 | -7.379E-3 | -8.069E-3 |
| 1.15 | -6.336E-3 | -6.224E-3 | -6.397E-3 | -6.735E-3 | -7.174E-3 | -7.674E-3 | -8.236E-3 | -8.867E-3 | -9.587E-3 | -1.042E-2 | -1.137E-2 |
| 1.20 | -8.601E-3 | -8.535E-3 | -8.812E-3 | -9.298E-3 | -9.918E-3 | -1.062E-2 | -1.140E-2 | -1.228E-2 | -1.327E-2 | -1.440E-2 | -1.568E-2 |
| 1.25 | -1.155E-2 | -1.156E-2 | -1.198E-2 | -1.264E-2 | -1.348E-2 | -1.442E-2 | -1.548E-2 | -1.666E-2 | -1.799E-2 | -1.950E-2 | -2.119E-2 |
| 1.30 | -1.535E-2 | -1.545E-2 | -1.604E-2 | -1.692E-2 | -1.801E-2 | -1.925E-2 | -2.063E-2 | -2.218E-2 | -2.393E-2 | -2.592E-2 | -2.811E-2 |
| 1.35 | -2.013E-2 | -2.036E-2 | -2.115E-2 | -2.230E-2 | -2.372E-2 | -2.532E-2 | -2.712E-2 | -2.912E-2 | -3.138E-2 | -3.393E-2 | -3.680E-2 |
| 1.40 | -2.610E-2 | -2.651E-2 | -2.757E-2 | -2.906E-2 | -3.084E-2 | -3.288E-2 | -3.516E-2 | -3.771E-2 | -4.058E-2 | -4.383E-2 | -4.742E-2 |
| 1.45 | -3.353E-2 | -3.414E-2 | -3.551E-2 | -3.740E-2 | -3.966E-2 | -4.223E-2 | -4.512E-2 | -4.835E-2 | -5.196E-2 | -5.603E-2 | -6.059E-2 |
| 1.50 | -4.264E-2 | -4.353E-2 | -4.529E-2 | -4.766E-2 | -5.046E-2 | -5.366E-2 | -5.726E-2 | -6.128E-2 | -6.582E-2 | -7.094E-2 | -7.664E-2 |
| 1.55 | -5.364E-2 | -5.485E-2 | -5.704E-2 | -5.995E-2 | -6.344E-2 | -6.741E-2 | -7.187E-2 | -7.686E-2 | -8.245E-2 | -8.878E-2 | -9.594E-2 |
| 1.60 | -6.673E-2 | -6.831E-2 | -7.102E-2 | -7.460E-2 | -7.888E-2 | -8.375E-2 | -8.919E-2 | -9.527E-2 | -1.021E-1 | -1.099E-1 | -1.187E-1 |
| 1.65 | -8.218E-2 | -8.419E-2 | -8.749E-2 | -9.184E-2 | -9.708E-2 | -1.030E-1 | -1.097E-1 | -1.171E-1 | -1.255E-1 | -1.350E-1 | -1.459E-1 |
| 1.70 | -1.004E-1 | -1.029E-1 | -1.069E-1 | -1.122E-1 | -1.185E-1 | -1.258E-1 | -1.338E-1 | -1.429E-1 | -1.531E-1 | -1.646E-1 | -1.780E-1 |
| 1.75 | -1.219E-1 | -1.249E-1 | -1.298E-1 | -1.361E-1 | -1.437E-1 | -1.525E-1 | -1.623E-1 | -1.732E-1 | -1.856E-1 | -1.997E-1 | -2.164E-1 |
| 1.80 | -1.470E-1 | -1.507E-1 | -1.564E-1 | -1.639E-1 | -1.731E-1 | -1.837E-1 | -1.954E-1 | -2.085E-1 | -2.234E-1 | -2.406E-1 | -2.615E-1 |
| 1.85 | -1.761E-1 | -1.806E-1 | -1.873E-1 | -1.963E-1 | -2.073E-1 | -2.199E-1 | -2.341E-1 | -2.499E-1 | -2.680E-1 | -2.893E-1 | |
| 1.90 | -2.097E-1 | -2.152E-1 | -2.232E-1 | -2.339E-1 | -2.468E-1 | -2.617E-1 | -2.786E-1 | -2.977E-1 | |||
| 1.95 | -2.483E-1 | -2.549E-1 | -2.644E-1 | -2.771E-1 | -2.923E-1 | -3.102E-1 | -3.308E-1 | ||||
| 2.00 | -2.925E-1 | -3.004E-1 | -3.116E-1 | -3.265E-1 | -3.446E-1 | ||||||
| 2.05 | -3.434E-1 | -3.527E-1 | -3.660E-1 | ||||||||
| 2.10 | -4.014E-1 | -4.124E-1 | |||||||||
| Table 8. Enthalpy of exitations (J g-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 |
4.174E-6 |
3.236E-6 |
2.618E-6 |
2.190E-6 |
1.874E-6 |
1.633E-6 |
1.443E-6 |
1.290E-6 |
1.164E-6 |
1.058E-6 |
9.670E-7 |
| 0.15 | 6.261E-6 | 4.855E-6 | 3.927E-6 | 3.285E-6 | 2.811E-6 | 2.449E-6 | 2.165E-6 | 1.936E-6 | 1.746E-6 | 1.587E-6 | 1.450E-6 |
| 0.20 | 1.181E-5 | 9.183E-6 | 7.449E-6 | 6.238E-6 | 5.343E-6 | 4.660E-6 | 4.122E-6 | 3.687E-6 | 3.328E-6 | 3.028E-6 | 2.771E-6 |
| 0.25 | 2.337E-5 | 1.826E-5 | 1.486E-5 | 1.247E-5 | 1.069E-5 | 9.335E-6 | 8.262E-6 | 7.395E-6 | 6.680E-6 | 6.082E-6 | 5.573E-6 |
| 0.30 | 4.412E-5 | 3.467E-5 | 2.832E-5 | 2.381E-5 | 2.045E-5 | 1.786E-5 | 1.582E-5 | 1.417E-5 | 1.280E-5 | ||