System with Variable Energy, Volume and Number of Particles: Evaluation of Partition Function and Thermodynamic Quantities

Partition function and thermodynamic parameters of the system open with respect to energy E, volume V and number of particles N, whereas temperature T, chemical potential μ and pressure P were kept constant, were considered by the procedure proposed by Gibbs. The mean values of variable energy, volume and number of particles were obtained by universal expression for such values. The entropy was determined by its general statistical definition. The thermodynamic potential and other thermodynamic quantities were also turned out naturally

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction

The stoichiometric network analysis (SNA) introduced by B.L.Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.SCOPUS: ar.jinfo:eu-repo/semantics/publishe