The Thermodynamic Properties of Helium Gas

The Joule-Thomson coefficients of the preceding article and the $\mathrm{pv}$ data of Holborn and Otto are here used to calculate the most important thermodynamic properties of helium. The variation of the specific heat with pressure is small. The computed values of the specific volumes compare excellently with those from the data of Holborn and Otto. Simple relationships are shown to exist between the coefficient of free expansion $\eta$ and the intrinsic energy variation $\lambda$. Convenient equations are derived for computing these coefficients. $\eta$ is independent of the pressure and $\lambda$ is proportional to the square of the pressure except at the lowest temperatures. Both $\eta$ and $\lambda$ are zero at about -70°C, are positive below this temperature and are negative above. Their numerical value above -70°C is everywhere small. The pressure and temperature behavior of $\eta$ and $\lambda$ is explained by a kinetic theory taking into account the change in the total potential energy stored by collision between the helium atoms when the pressure is altered. The law of force between two helium atoms, consistent with this theory, is of the type giving rise to the same mutual potential energy of two helium atoms as deduced from considerations of the quantum theory. It is extremely doubtful that the trend of $\eta$ at high temperature leads ultimately to the perfect gas state.