Page 26 - Thermodynamics of Biochemical Reactions

20 Chapter 2 Structure of Thermodynamics

in a spontaneous process. For example, the internal energy of an isolated system
decreases when a spontaneous process occurs in it because S and V are constant.
If thermodynamics could not provide more than this, it would be difficult to use.
Fortunately mathematics provides a way to introduce intensive variables as
independent variables by using Legendre transforms.
The concept of a Legendre transform is very important because it leads
from the internal energy U to the enthalpy H and the Gibbs energy G;
these thermodynamic properties are defined by H = U + PI/ and G =
U + PV - TS = H - TS. In this book additional Legendre transforms are used
to define the transformed Gibbs energy G' and the transformed enthalpy H' at
specified pH and pMg in Chapter 4 on biochemical reactions. In Chapter 6
further transformed Gibbs energies G" and further transformed enthalpies H" are
introduced to discuss systems of biochemical reactions at specified concentrations
of coenzymes. The construction of Legendre transforms is discussed in Section 2.5.
It is also important to understand that all these properties obey all the rules
of calculus. As a consequence these properties are related through fundamental
equations, Maxwell equations, Gibbs-Helmholtz equations, and Gibbs-Duhem
equations.
The internal energy U, entropy, and the properties defined by Legendre
transforms are referred to as thermodynamic potentials because, like the potential
energy in mechanics, these extensive properties of a thermodynamic system give
information about the direction of spontaneous change and the equilibrium state
of the system. When work other than pressure-volume work is involved in a
system, still more thermodynamic potentials can be defined by use of Legendre
transforms, and these thermodynamic potentials provide criteria of equilibrium
when sets of properties convenient for the experimenter are held constant. These
various thermodynamic potentials are needed for the convenience of the experi-
menter. The thermodynamic potential used to provide a criterion of spontaneous
change and equilibrium depends on the intensive variables that are held constant.
Biochemical systems provide exceptional challenges to thermodynamics because
the concentrations of hydrogen ions, certain metal ions, and coenzymes may be
held constant, and electrical work, mechanical work, and surface work may be
involved in addition to chemical work and PV work. When the equations in this
chapter are applied to dilute electrolyte solutions, it is convenient to take the
thermodynamic properties to be functions of the ionic strength. This is not treated
in detail in this chapter, but is in the next chapter.
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 ther-
modynamics 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).

2.1 STATE OF A SYSTEM

A system that is made up of a homogeneous mass of a substance at equilibrium
can be described as being in a certain thermodynamic state that is characterized
by certain properties. If forces of various types act on the system or more of the
substance is added, the system is changed to a different state. It is remarkable that
only a small number of properties have to be specified to completely characterize
the equilibrium state of a macroscopic system. For a system containing a single
substance, three properties suffice, if they are properly chosen. For example, the