Calculations of the second derivatives of the thermodynamic functions of pure substances in the vicinity of the critical point according to the van der waals equation

The second derivatives inverse to derivatives in the known sets of critical conditions were studied analytically at the critical point. All of them were shown to take on infinite values at the critical point. The special features of discontinuities of some of these derivatives in the critical state were revealed by numerical methods. The conclusions obtained are valid for any model of the unified equation of state of pure substances.