Thermodynamic equilibrium, criterion constant pressure

To illustrate the use of this equilibrium criterion, consider the very simple, initially nonuniform system shown in Fig. 7.1-1. There a single-phase, single-component fluid in an adiabatic, constant-volume container has been divided into two subsystems by an imaginary-boundary. Each of these subsystems is assumed to contain the same chemical species of uniform thermodynamic properties. However, these subsystems are open to the flow of heat and mass across the imaginary internal boundary, and their temperature and-pressure need not be the same. For the composite system consisting of the two subsystems, the total mass (though, in fact, we will use number of moles), internal energy, volume, and entropy, all of which are extensive variables, are the sums of these respective quantities for the two subsystems, that is. 

The following criterion of phase equilibrium can be developed from the first and second laws of thermodynamics the equilibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

Thermodynamics is used to predict whether reactants have a spontaneous tendency to change into products. This tendency is associated with a decrease in the free energy or Gibbs energy of the system (G) to a minimum. As a consequence, the thermodynamic criterion for spontaneous change at constant temperature and pressure is AG < 0. Under standard conditions (concentrations = 1 M, and P = 1 atm), the standard Gibbs energy variation (AG°) is related with the equilibrium constant (A) by equation 11 ... 

The thermodynamic criterion for the equilibria CaCO, ) = Ca0(,) + C02 (,) is AG ° = -RT n Kp, where AG° is the change in Gibbs free energy of the reactants and products in their standard state, R is the gas constant, and Kp is the equilibrium constant. For this equilibria, A p = pco, for pressure in units of atmospheres. Values for AG are tabulated in the form AG° = a+ bT combining these expressions yields an exponential relationship between the partial pressure of CO2 and temperature for the above equilibria. Complete derivations and discussion of these equations may be found in physical chemistry textbooks such as references [13] and [14]. 

There are five linear hydrodynamic equations containing the seven fluctuations (pi, u x,ii y, uu,pi,si, 7i). The local equilibrium thermodynamic equations of state can be used to eliminate two of the four scalar field quantities (pi, si, Ti, pi). In this chapter we chose the temperature and number density as independent variables, although we could equally well have chosen the pressure and entropy. One useful criterion for choosing a particular set is that the equilibrium fluctuations of the two variables be statistically independent. The two sets (pi = dp, T = ST) and (pi = Sp, si = Ss) both involve two variables that are statistically independent, that is, statistical independence of the two variables simplifies our analysis considerably. It is particularly convenient to chose the set (Pi,Ti) over the set (pi, si) because the dielectric constant derivatives (de/dp)T and (de/dT) are more readily obtained from experiment (other than light scattering) than are (ds/dS)p and (ds/dp)s-... 

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