In 1963-64 Mark Kac and others in a set of three papers established that Van der Waals equation of state, originally formulated on empirical basis, can be derived from Principles of Thermodynamics and Statistical Mechanics (see M. Kac, G. Hhlenbeck, P. Hemmer, On the van der Waals theory of vapor-liquid equilibrium, I, II, III). The demonstration is based on series of rigorous applications of probability partition functions.
Are there more simple mathematical proofs of the fact that non-ideal equations of state F(p, V, T) = 0 for solid, liquid and gas can be deducted from basic Principles of Thermodynamics or Newton's Principles (as done for ideal gas law pV = kT)?
Gianluca
No-the equation of state is the starting point of the description of the thermodynamic, i.e. collective, properties of a gas. It can only be derived from a model of the underlying microscopic degrees of freedom-which is what statistical mechanics is about.
What can be checked is whether a given equation of state does describe stable matter. One test is that the pressure is positive, for instance and what happens if it becomes negative.
That is correct: Constitutive properties cannot be derived from "Basic
Principles ofThermodynamics" because these principles are valid for all
materials. Consequently, you need additional constitutive presupposition.
No.Non ideallity in condensed matter (gases,liquids,solids) is caused by the interactions of their constituents (atoms,ions,molecules).Approximate equations of state are derived for specific structural models of the constituents and their interactions plus specific statistical approximations used to treat the many body problem or computer simulations (MD,MC).The principles of statistical physics and thermodynamics in the classical or quantum regime,just provide the framework of conditions these approximate theories have to fulfill in order to be acceptable ,useful descriptions.
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