Thermodynamic stability of multicomponent ideal gas

TL;DR

This paper challenges the traditional understanding of thermodynamic equilibrium in multicomponent ideal gases by providing thought experiments that demonstrate equilibrium states can be determined with fewer variables than Gibbs' phase rule suggests.

Contribution

It presents a counterexample to the conventional rule, showing that equilibrium states in multicomponent ideal gases may be characterized by fewer variables than previously thought.

Findings

Equilibrium states can be determined with fewer variables in certain ideal gas mixtures.

The results apply to systems with more than two components.

Challenging Gibbs' phase rule in specific idealized scenarios.

Abstract

We present an example counter to the widely-accepted concept on equilibrium states that "Any thermodynamic equilibrium state of two component systems is determined by specifying 4 thermodynamic variables that include at least 1 extensive variable." which is equivalent to Gibbs' phase rule. We demonstrate this fact by thought experiments on an A/B binary mixture where temperature, pressure and chemical potential of the A-species are chosen as the 3 intensive variables while the number of B-molecules is chosen as the 1 extensive variable. Our findings also apply to $M (>2)$-component systems.