# 6: Equilibrium States and Reversible Processes

• 6.1: The Thermodynamic Perspective
Classical thermodynamics does not consider the atomic and molecular characteristics of matter. In developing it, we focus exclusively on the measurable properties of macroscopic quantities of matter. In particular, we study the relationship between the thermodynamic functions that characterize a system and the increments of heat and work that the system receives as it undergoes some change of state. In doing so, we adopt some particular perspectives.
• 6.2: Thermodynamic Systems and Variables
We characterize the system by specifying the values of enough variables so that the system can be exactly replicated. By “exactly replicated” we mean, of course, that we are not able to distinguish the system from its replicate by any experimental measurement. Any variable that can be used to characterize the system in this way is called a variable of state, a state variable, or a state function.
• 6.3: Equilibrium and Reversibility - Phase Equilibria
We call any process whose direction can be reversed by an arbitrarily small change in a thermodynamic state function a reversible process. Evidently, there is a close connection between reversible processes and equilibrium states. If a process is to occur reversibly, the system must pass continuously from one equilibrium state to another.
• 6.4: Distribution Equilibria
A system can contain more than one phase, and more than one chemical substance can be present in each phase. If one of the substances is present in two phases, we say that the substance is distributed between the two phases. We can describe the equilibrium distribution quantitatively by specifying the concentration of the substance in each phase. At constant temperature, we find experimentally that the ratio of these concentrations is approximately constant.
• 6.5: Equilibria in Chemical Reactions
Equilibria involving chemical reactions share important characteristics with phase and distribution equilibria.
• 6.6: Le Chatelier's Principle
If we start with a system that is at equilibrium, and we impose a change in conditions on it, the “initial” state of the system after the imposed change of conditions will generally not be an equilibrium state. Experience shows that the system will undergo some spontaneous change to arrive at a new equilibrium state. In these particular circumstances, Le Chatelier’s principle enables us to predict the spontaneous change that occurs.
• 6.7: The Number of Variables Required to Specify Some Familiar Systems
In the experiment or in the mathematical model, fixing two of the three intensive variables is sufficient to fix the equilibrium properties of the system. Fixing the equilibrium properties means, of course, that the state of the system is fixed to within an arbitrary factor, which can be specified either as the number of moles present or as the system volume.
• 6.8: Gibbs' Phase Rule
Gibbs found an important relationship among the number of chemical constituents, the number of phases present, and the number of intensive variables that must be specified in order to characterize an equilibrium system. This number is called the number of degrees of freedom available to the system and is given the symbol F . By specifying F intensive variables, we can specify the state of the system—except for the amount of each phase.
• 6.9: Reversible vs. Irreversible Processes
A process that is not reversible is said to be irreversible. We distinguish between two kinds of irreversible processes. A process that cannot occur under a given set of conditions is said to be an impossible process. A process that can occur, but does not do so reversibly, is called a possible process or a spontaneous process.
• 6.10: Duhem's Theorem - Specifying Reversible Change in A Closed System
• 6.11: Reversible Motion of A Mass in A Constant Gravitational Field
Let us explore our ideas about reversibility further by considering the familiar case of a bowling ball ball that can move vertically in the effectively constant gravitational field near the surface of the earth.
• 6.12: Equilibria and Reversible Processes
The distinction between a system at equilibrium and a system undergoing reversible change is razor-thin. What we have in mind goes to the way we choose to define the system and centers on the origin of the forces that affect its energy. For a system at equilibrium, the forces are fixed. For a system undergoing reversible change, some of the forces originate in the surroundings, and those that do are potentially variable.
• 6.13: The Laws of Thermodynamics
We usually consider that the first, second, and third laws of thermodynamics are basic postulates. One of our primary objectives is to understand the ideas that are embodied in these laws. We introduce these ideas here, using statements of the laws of thermodynamics that are immediately applicable to chemical systems. In the next three chapters, we develop some of the most important consequences of these ideas.
• 6.14: Thermodynamic Criteria for Change
When the state of an isolated system can change, we say that the system is capable of spontaneous change. When an isolated system is incapable of spontaneous change, we say that it is at equilibrium. Ultimately, this statement defines what we mean by (primitive) equilibrium.
• 6.15: State Functions in Systems Undergoing Spontaneous Change
• 6.16: Problems

Thumbnail: Illustration of a system exhibiting an irreversible process as rapid and slow particles mix together. (CC BY 2.5 Generic; Htkym and Dhollm via Wikipedia)