Spontaneous change defined

The first two parts of this book explain how scientists now understand normal alterations of consciousness in brain chemical terms. In part I, The Scope and Shape of Conscious States, I define the psychological components and dimensions of conscious experience. Chapter 1 shows how subjective experience can be conceptualized and measured in relation to brain science. It also introduces the notion of a unified brain-mind. Chapter 2 emphasizes the strategy of studying both spontaneous and experimental alterations in conscious state. Chapter 3 contrasts waking and dreaming by illustrating the way that we can measure these dramatic spontaneous changes in conscious state. 

CHEMICAL ELEMENTS. A chemical element may be defined as a collection of atoms of otic type which cannot be decomposed into any simpler units by any chemical transformation, but which may spontaneously change into other units by radioactive processes A chemical element is a substance that is made up of but one kind of atom. Of the over 100 chemical elements known, only 90 tire found in nature. The remaining elements have been produced in nuclear reactors and particle accelerators. Theoretical physicists do not all agree, but some believe that fission-stable nuclei should exist at atomic numbers 109. 114. and 126. Claims thus lur have been made for the discovery, isolation, or creation of elements up to 110. The element with the highest atomic number officially named and entered into the formal table of atomic weight is darmstudlium (Dx) with an atomic number of 110. 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

The reason for going into this much detail on all of the thermodynamic potentials that can be defined for a one-phase, one-species system and the corresponding criteria for spontaneous change is to illustrate the process by which these thermodynamic potentials are defined and how they provide criteria for... 

The Legendre transform that defines the further transformed Gibbs energy G", which provides the criterion for spontaneous change and equilibrium in dilute... 

Since coenzymes, and perhaps other reactants, are in steady states in living cells, it is of interest to use a Legendre transform to define a further transformed Gibbs energy G" that provides the criterion for spontaneous change and equilibrium at a specified pH and specified concentrations of coenzymes. This process brings in a further transformed entropy S" and a further transformed enthalpy H", but the relations between these properties have the familiar form. 

The second law requires that, for a spontaneous change at constant temperature and volume, dF < 0. Alternatively, under conditions of constant temperature and pressure gives dG < 0. That is, the total free energy of the system decreases spontaneously at constant T and P until it reaches a minimum at equilibrium, dG = 0. The minimization of the Gtotai is one of two criteria defining an equilibrium state. 

We need to understand the concepts of Gibbs free enei gy (G) and chemical potential i/i) in order to know the direction of spontaneous change of a reaction or system. These concepts can also be used to define or predict the most stable (equilibrium) assemblage and gas, fluid, or rock compositions expected in a system at a given pressure and temperature. Some phases and aqueous species in a system may be out of equilibrium with that system. Free-energy calculations permit us to decide which substances are out of equilibrium, and, therefore, which concentrations may be governed by chemical kinetics. 

There Is only one way for a system to be In equilibrium with its surroundings. There are many ways to be out-of-equilibrium. Therefore, the field of thermostatics is well-defined and mature, and the field of thermodynamics (or irreversible thermodynamics or whatever latest fashion calls it) is less well-defined and growing. By irreversible thermodynamics, we usually mean the study of processes in which spontaneous change is occurring and, therefore, thermostatic entropy is being created. Since, by definition the system is not in equilibrium, the central question is how to relate the entropy change to physical processes other than the definition in Equation 2, since that definition requires "reversible heat transfer."... 

Spontaneous processes may occur in such a system when it is not at equilibrium with a consequent decrease in the free energy. When A is a minimum and dA = 0 no further spontaneous changes can occur and the system is at equilibrium. Again we see the parallel between the free energy A and the potential energy in a mechanical system. If the latter system is not harnessed to do work the position of equilibrium could be defined in terms of minimum energy. 

Furthermore, Equation 5.23 shows that entropy is a state function that can be defined on the basis of the properties of the system. 8 does not depend on the way a state was achieved, however. Like internal energy, entropy is a state function. This is in fact the second law of thermodynamics. The same final state with entropy 8 can be achieved either by spontaneous change or by performing work. 

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