Structure of Thermodynamics

The equations and calculations described in this chapter are very useful, but so far we have not discussed thermodynamic properties other than equilibrium constants. The other properties introduced in the next three chapters provide a better understanding of the energetics and equilibria of reactions. We will consider the basic structure of thermodynamics in Chapter 2 and then to apply these ideas to chemical reactions in Chapter 3 and biochemical reactions in Chapter 4. 

This chapter deals with the thermodynamics of one-phase systems, and it is understood that the phase is homogeneous and at uniform temperature. The basic structure of thermodynamics provides the tools for the treatment of more complicated systems in later chapters. This book starts with the fundamentals of thermodynamics, but the reader really needs some prior experience with thermodynamics at the level of undergraduate thermodynamics (Silbey and Alberty, 2001). Legendre transforms play an important role in this chapter, and the best single reference on Legendre transforms is Callen (1960, 1985). Other useful references for basic thermodynamics are Tisza (1966), Beattie and Oppenheim (1979), Bailyn (1994), and Greiner, Neise, and Stocker (1995). 

Our initial purpose in this chapter is to develop from the first and second laws the fundamental property relations which underlie the mathematical structure of thermodynamics. From these, we derive equations which allow calculation of enthalpy and entropy values from PVT and heat-capacity data. We then discuss the diagrams and tables by which both measured and calculated property values are presented for convenient use. Finally, we develop generalized correlations which allow estimates of property values to be made in the absence of complete experimental information. 

It is assumed that the reader has had some introduction to thermodynamics at the level of an undergraduate course in physical chemistry. My previous book "Thermodynamics of Biochemical Reactions," Wiley, Hoboken, NJ (2003) provides a more complete introduction to the structure of thermodynamics and its relation to statistical mechanics. This successor book is needed because more recent research has clarified the structure of biochemical thermodynamics and opened up new possibilities for learning about the flow of energy in living things. Three aspects of these calculations are as follows ... 

THERMODYNAMICS TABLE 4 1 Mathematical Structure of Thermodynamic Property Relations... 

So the third law and zeroth law were named. Now it seems clear that a lot of other input is needed to get the entire structure of thermodynamics and apply it in the real world. Let s hope people have given up numbering laws. 

An objective, of this book is to present the subject of thermodynamics in a logical, coherent manner. We do this by demonstnuing how the complete structure of thermodynamics can be built from a number of important experimental observations, some of which have been introduced in this chapter, some of which are familiar from mechanics, and some of which are introduced in the following chapters. For convenience, the most important of these observations are listed here. 

Obviously the first law is not all there is to the structure of thermodynamics, since some adiabatic changes occur spontaneously while the reverse process never occurs. An aspect of the second law is that a state function, the entropy S, is found that increases in a spontaneous adiabatic process and remains unchanged in a reversible adiabatic process it cannot decrease in any adiabatic process. 

QS AR) represents an attempt to correlate structural or property descriptors of compounds with reactivities (Topliss, 1983 Hansch and Hoekman, 1995). An explanation of the struc-tnral effect on the eqnilibria or rates of chemical reactions often involve some kind of comparison with a snitable model or set of models. The quantities compared are thermodynamic, nsnally free energies, enthalpies or entropies, but the simple relationships found among snch qnantities are often not part of the formal structure of thermodynamics, hence they are referred to extrathermodynamic relationships. Useful extrathermodynamic relationships are nsnally simple in form. The mathematical simplicity of many extrathermo-dynamic relationships resnlts from the tendency of such quantities to be additive functions of molecular structure. The molar values of the property under comparison are assumed to be approximately additive functions of independent contributions assignable to substructures of the molecules. 

Legendre transforms show us the general mathematical structure of thermodynamics. Clearly there are more Legendre transforms that can be defined, not only of U S,V,Nk) but also of S U,V,Nk) of S U,V,Nk). A detailed presentation of the Legendre transforms in thermodynamics can be found in the text written by Herbert Callen [3]. (Legendre transforms also appear in classical mechanics the Hamiltonian is a Legendre transform of the Lagrangian.)... 

It is a very old empirical fact that the thermal processes in nature are submitted to certain restrictions, which strongly limit the class of feasible processes. The exact and sufficiently general formulation of these restrictions is extremely difficult and sometimes even incorrect, e.g., the principle of Antiperistasis [195], Braun-le Chatelier s principle [196] as well as the second law itself but, in spite of it, are found very useful. That is why we believe [197] that the Second Law, as well as other laws which put analogous limitations on thermal processes, reflects experimental facts with an appreciable accuracy and thus it should be aptly incorporated into the formalism of thermodynamics. On the other side, being aware of the fact that the contemporary structure of thermodynamics with its somehow archaic conceptual basis may have intrinsic flaws, we venture to claim that the absolute status of the Second Law should... 

The mathematical structure of thermodynamics is based on two laws. The third law, also called Nernst s heat theorem, properly belongs to statistical theory. Its main use in thermodynamics is in establishing an entropy scale. In 1931 Fowler raised the postulate regarding the existence of thermal equilibrium to the status of the zeroth law of thermodynamics. We need discuss neither the zeroth or the third laws here. 

---