Thermodynamic principles

An atmospheric air parcel can be viewed thermodynamically as a homogeneous system that may exchange energy, work, and mass with its surroundings. Let us assume that an air parcel contains k chemical species and has a temperature T. pressure p, and volume V. There are n,- moles of species i in the parcel. 

The first section of this chapter is a review of fundamental chemical thermodynamic principles focusing on the chemical potential of species in the gas, aqueous, and solid phases. Further discussion of fundamentals of chemical thermodynamics can be found in Denbigh (1981). Chemical potentials form the basis for the development of a rigorous mathematical framework for the derivation of the equilibrium conditions between different phases. This framework is then applied to the partitioning of inorganic aerosol components (sulfate, nitrate, chloride, ammonium, and water) between the gas and particulate phases. The behavior of organic aerosol components will be discussed in Chapter 14. 

Let us consider a closed system with/phases and k components that do not react mutually. The composition of each phase can be expressed using A — 1 molar fractions, since it holds that the sum of the mole fractions in each phase is equal to 1. 

For the description of /-independent phases with k components, we therefore need f(k - 1) independent data on composition. To these we still have to add data on temperature and pressure, so we have altogether/( - l) + 2 intensive data, if the temperature and pressure are equal in the whole system. If the system considered is in equilibrium, the intensive criterion of the thermodynamic equilibrium must be fulfilled, fhus the chemical potentials of all the k components in all the/phases have to be equal. This criterion thus defines fhe number of binding conditions between the intensive variables. This number is kif- 1), because the number of binding conditions is one less than the number of phases. Then the difference between both the quantities defines the number of intensive variables, which are independent in a system with A components and/phases being in equilibrium -the variance, or the number of degrees of freedom v 

This is the mathematical expression of the Gibbs phase law. It is an explicit and simple guide in the study of phase equilibria. 

A closed vessel filled with gaseous oxygen. 

The system has two degrees of freedom, we can change the temperature and pressure without the occurrence of a new phase. 

The entropy principle emerges from the conception of the world as a chaos of particles endowed with random motions. It states that when any system undergoes a small displacement from equilibrium the heat taken in, dQ, is related to the entropy change by the 

Such a change is called reversible for the irreversible change 

These relations hold whether the molecules exert forces on one another or whether they are nearly independent masses as, approximately, are those of dilute gases. When mutual influences are not negligible, then the internal energy becomes a function of the volume. In general it may also be a function of other external variables. 

The question of the relation between the heat changes accompanying various kinds of natural process and the work which may be performed is one that has been of dominating importance. The conception of the statistical entropy is evidently one which penetrates more deeply into the nature of things, but the idea of deriving work from heat is one which has appealed more strongly to minds bent upon the useful arts such as the construction of steam-engines, and the laws of thermodynamics were discovered independently of the statistical ideas which interpret them. 

The flrst law of thermodynamics states that there is an exact quantitative equivalence between heat consumed and mechanical work generated and vice versa. In the light of the notion that heat is the invisible energy of molecules, differing only from mechanical 

Our starting point is the Flory-Huggins free energy for a mixture of two polymer species (with degrees of polymerization N/, Nb). This is a natural generalization of eq. (III.l) 

How do we discuss phase separation on the free energy F( ) The essential property is the curvature of F( ), as explained in Fig. IV.2. 

Assume first that e sample is homogeneous (single phase), with a certain concentration d (point J). Try then to decompose it into two phases, of concentrations 4 i and 2- The relative weights of the two phases in the mixtures are/i and. We then have 

This corresponds to point J in Fig. IV.2. The energy change is positive in case (a) and negative in case (b). Thus, case (b) imposes phase separation.  

In case (a) near a concentration we have local stability, but we may still have an instability with respect to another branch of the phase diagram. This will become apparent in the plots of the Flory-Huggins free energy [eq. (IV.6)] (Fig. IV. 3). 

1 Standard free energy of formation versus temperature diagrams 

Vapor species that form in any given high-temperature corrosion situation often have a strong influence on the rate of attack, the rate generally being accelerated when volatile corrosion products form. Gulbransen and Jansson have shown that metal and volatile oxide species are important in the kinetics of high-temperature oxidation of carbon, silicon, molybdenum, and chromium. Six types of oxidation phenomena were identified  

At low temperature, diffusion of oxygen and metal species through a compact oxide film 

At moderate and high temperatures, a combination of oxide film formation and oxide volatility 

TABLE 3.1 Thermodynamic Data for Reactions Involving Oxygen 

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Thermodynamic principles govern all air conditioning processes (see Heat exchange technology, heat transfer). Of particular importance are specific thermodynamic appHcations both to equipment performance which influences the energy consumption of a system and to the properties of moist air which determine air conditioning capacity. The concentration of moist air defines a system s load. 

Solely on the basis of thermodynamic principles, which method would you recommend Show calculations. 

If the present volume will help towards the comprehension of the fundamental principles on which the science of thermodynamics rests, and also serve to bring home the importance of a knowledge of these principles in the suggestion and interpretation of experimental work, the purpose which has been kept in view during its preparation will have been amply fulfilled. In any case, it is hoped that neither the extreme view that thermodynamic principles alone suffice in the construction of a systematic physical or chemical science, nor the equally mistaken opinion that they are of little practical utility to the experimental worker, can fairly result from its study. 

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