Page 44 - Advanced Thermodynamics for Engineers, Second Edition

28 CHAPTER 2 THE SECOND LAW AND EQUILIBRIUM

shown in Fig. 2.5. Equilibrium of mixtures of elements and compounds is defined by the state of
maximum entropy or minimum Gibbs or Helmholtz energy; this is discussed in Chapter 12. The
concepts of stable equilibrium can also be used to analyse the operation of fuel cells and these are
considered in Chapter 21.
Another form of equilibrium met in thermodynamics is metastable equilibrium. This is where a
system exists in a ‘stable’ state without any tendency to change until it is perturbed by an external
influence through a finite perturbation. A good example of this is met in combustion in spark-ignition
engines, where the reactants (air and fuel) are induced into the engine in a premixed form. They are
ignited by a small spark and convert rapidly into products, releasing many thousands of times the
energy of the spark used to initiate the combustion process. Another example of metastable equilib-
rium is encountered in the Wilson ‘cloud chamber’ used to show the tracks of a particles in atomic
physics. The Wilson cloud chamber consists of supersaturated water vapour which has been cooled
down below the dewpoint without condensation – it is in a metastable state. If an a particle is
introduced into the chamber it provides sufficient perturbation to bring about condensation along its
path. Other examples include explosive boiling which can occur if there are not sufficient nucleation
sites to induce sufficient bubbles at boiling point to induce normal boiling, and some of the crystalline
states encountered in metallic structures.
Unstable states cannot be sustained in thermodynamics because the molecular movement will tend
to perturb the systems and cause them to move towards a stable state. Hence, unstable states are only
transitory states met in systems which are moving towards equilibrium. The gases in a combustion
chamber are often in unstable equilibrium because they cannot react quickly enough to maintain the
equilibrium state, which is defined by minimum Gibbs or Helmholtz energy. The ‘distance’ of the
unstable state from the state of stable equilibrium defines the rate at which the reaction occurs; this is
referred to as rate kinetics, and will be discussed in Chapter 14. Another example of unstable ‘equi-
librium’ occurs when a partition is removed between two gases which are initially separated. These
gases then mix due to diffusion, and this mixing is driven by the difference in chemical potential
between the gases; chemical potential is introduced in Chapter 12 and the process of mixing is dis-
cussed in Chapter 20. Some thermodynamic situations never achieve stable equilibrium, they exist in a
steady state with energy passing between systems in stable equilibrium, and such a situation can be
analysed using the techniques of irreversible thermodynamics developed in Chapter 20.

2.13.1 SIGNIFICANCE OF THE MINIMUM GIBBS ENERGY AT CONSTANT
PRESSURE AND TEMPERATURE

It is difficult for many mechanical engineers to readily see the significance of Gibbs and Helmholtz
energy. If systems are judged to undergo change while remaining in temperature and pressure equi-
librium with their surroundings then most mechanical engineers would feel that no change could have
taken place in the system. However, consideration of Eqn (2.30) shows that, if the system were a
multicomponent mixture, it would be possible for changes in Gibbs (or Helmholtz) energies to take
place if there were changes in composition. For example, an equilibrium mixture of carbon dioxide,
carbon monoxide and oxygen could change its composition by the carbon dioxide breaking down into
carbon monoxide and oxygen, in their stoichiometric proportions; this breakdown would change the
composition of the mixture. If the process happened at constant temperature and pressure, in equi-
librium with the surroundings, then an increase in the Gibbs energy, G, would have occurred; such a