HEPAK Specifications…


HEPAK is a series of physics-based fundamental state equations for calculating the thermophysical properties of helium-4 (4He), including liquid helium calculations for helium I (below the boiling point and above the lambda point) and the superfluid condition of helium II (below the lambda point).

The state equations are valid from 0.8 K or the melting line to 1,500 K, including the superfluid range, the lambda line, and liquid vapor mixtures.  As a function of pressure, calculations are valid up to 1,000 bars, and between 80 and 300 K where they are valid to 20,000 bars.

Current HEPAK development targets improvements in algorithm transitions around the critical point and near the lambda line, and new work that extends property calculations below the current temperatures limit of 0.8 K.

Calculated state properties include:

  • PVT
  • Enthalpy, Entropy, Gibbs and Internal Energy
  • Specific Heats
  • Sound Velocity, including 2nd and 4th sound velocity in the superfluid
  • Compressibility
  • Joule-Thomson coefficient
  • Expansivity
  • Gr√ľneisen parameter
  • Latent Heat
  • dP/dT of the saturation line
  • …plus several other PVT derivatives
  • Lambda line location as a function of P, V or T
  • Normal fluid density fraction in helium II
  • Mutual friction and conductivity function in helium II
  • State properties (as listed above) within micro degrees of the Lambda line

Other calculated properties include:

  • Viscosity down to 1.2 K
  • Thermal Conductivity down to 3 K
  • Dielectric Constant
  • Refractive Index
  • Fluid Surface Tension

A total of 41 pairs of input parameters (i.e., pressure and temperature, density and internal energy, saturation line and entropy) are available for specifying the fluid state. Included in the input parameter list are both isochoric and isobaric delta-T to the lambda line, valid for delta-T as small as 50 microkelvin.

HEPAK was written by Vincent Arp, Bob McCarty, and Jeff Fox, formerly of NIST and later of Cryodata, using code from Brian Hands while at the Oxford University Cryogenics Laboratory. HEPAK is referenced to NIST Technical Note 1334 (1989), by Arp and McCarty and an update of NIST Technical Note (1998) by D.G. Friend, V. Arp, and R.D. McCarty.

HEPAK is fully consistent with the updated NIST standard reference data for helium. It is also consistent with the International Temperature scale of 1990, defined by helium vapor pressure from 1.2 to 5.0 K.


Currently, HEPAK is offered:

  • As an Excel Add-In (works in 32bit and 64bit Excel and Windows OS) function access to property calculations extensively tested on version of Excel from Excel97 through Excel 2016.  The Excel Add-In has also been tested on the MAC Excel 2011 version with property calculations working correctly and occasional messaging glitches that are currently being debugged.
  • CURRENTLY SUSPENDED FOR RE-WRITE As an ActiveX DLL for interfacing to a variety of Windows programs. This version is delivered with sample interface code illustrating how to interface your own application to the GASPAK properties.
  • Fortran Source Code (will be suspended once ActiveX DLL re-write is completed).