(621f) Derivation of Equations of State by Discrete Modelling of Entropy

Entropy is the basic thermodynamic state variable in order to understand the behaviour of systems consisting of a huge number of particles like gases and liquids. In conjunction with Gibbs’ thermodynamics it can be used to deduce equations of state, one of the building blocks in chemical engineering. They provide the theoretical fundamentals for specifying and estimating the properties of gases and liquids. There are several classical approaches in order to deduce an equation for correlating dependencies between pressure and temperature of a gas and the volume it needs: empirical deductions (ideal gas), mathematical constructs (viral equation), and statistical approaches (Boltzmann statistics).

The method

The proposed algorithm consists in a simple approach which combines the Gibbs’ fundamental equation with discrete modelling of the state variables S, U, V and N. For modelling the entropy term we use information theory. Essential in this approach is that the four state variables are modelled using the same inner variables. The Gibbs’ fundamental equation builds the glue between the state variables and will lead to constraints that finally lead to the Maxwell-Boltzmann distribution of energies, and additionally to the ideal gas law.

Application

In this paper it will be demonstrated how modelling is done, especially for the inner energy and the entropy for which we need information theory. Following the mathematical constraints given by the Gibbs’ fundamental equation this leads in a first approach to the ideal gas law and at the same time to a distribution of energy comparable to the well-known Maxwell-Boltzmann distribution. These results build important criteria for the quality of approach. Finally approach can be extended to modelling of real gas.