Anomalous Transport Properties of a van der Waals Gas

The contribution of the long-range potential to the transport coefficients of a van der Waals gas in the critical region are calculated using the time-correlation-function method. The microscopic currents are expanded in terms of wave-vector-dependent density fluctuations (found previously by van Kampen) whose time dependence is assumed to be described by the linearized hydrodynamic equations. Self-consistent solutions for the thermal conductivity and volume viscosity are found to diverge near the critical point. The fluctuation correction to the specific heat at constant volume is found to diverge as | T − Tc | −1 / 2. The fluctuation correction to the equation of state yields a critical point for the system which differs from the critical point of the van der Waals equation of state. In as much as the divergence in the specific heat occurs at the van der Waals critical temperature rather than at the true critical temperature, these calculations are to be viewed as indicative of the qualitative behavior of a gas in the critical region, not too near the critical point.