A method of calculating the numerical equation of state for helium below 6 absolute, and of estimating the relative importance of gas degeneracy and inter-atomic forces

Abstract

Gas (the effect of non-Maxwellian distribution of molecular velocities) is distinguished from gas (the effect of intermolecular forces), and it is shown that specific heat measurements cannot be used to verify theories of the former, unless account is taken of the very rapid increase of the latter at the lowest temperatures and highest pressures. Accordingly a thermodynamic method is used to calculate the sum of degeneracy and imperfection at 4° and 5° Abs. for helium. Theories of degeneracy can then be roughly tested by the extent to which they allow a residual value of the imperfection to be calculated, and determine a consistent extension of the course taken by isothermals down to 15°. The method is applied to Fermi's expressions for degeneracy, and also to Berthelot's equation of state. One of the equations alone satisfies the required condition; it is shown that on this basis degeneracy would comprise 15 per cent. of the total departure of helium from the ideal gas laws at 4° and 5°, the remainder being due to true imperfection or intermolecular forces.