Thermodynamics physical statements

The second law of thermodynamics, like the first, represents a generalization of the results of a large number of experiments. In Sec. 4-1 we present two equivalent physical statements of the second law. In Sec. 4-2 we present the mathematical statement of the second law and determine how a criterion for equilibrium can be set up, making use of the mathematical statement. In Sec. 4-3 the mathematical statement of the second law is shown to be equivalent to the physical statements. The argument proceeds by demonstrating that Caratheodory s principle can be derived from the physical statements. 

The main purpose of this book is to present a rigorous and logical discussion of the fundamentals of thermodynamics and to develop in a coherent fashion the application of the basic principles to a number of systems of interest to chemists. The concept of temperature is carefully discussed, and special emphasis is placed on the appropriate method for the introduction of molecular weights into thermodynamics. A new treatment of the second law of thermodynamics is presented which demonstrates that Caratheodory s principle is a necessary and sufficient consequence of the physical statements of Clausius and Kelvin. 

The plan of the remaining sections of this chapter is as follows. In Sec. 4.3, a h)q)o-thetical device called a Carnot engine is introduced and used to prove that the two physical statements of the second law (the Clausius statement and the Kelvin-Planck statement) are equivalent, in the sense that if one is true, so is the other. An expression is also derived for the efficiency of a Carnol engine for Ihe purpose of defining thermodynamic temperature. Section 4.4 combines Carnot cycles and the Kelvin-Planck statement to derive the existence... 

There are two principal physical statements of the second law of thermodynamics (1) If a system undergoes a cyclic process it cannot turn heat put into the system completely into work done on the surroundings. (2) Heat cannot flow spontaneously from a cooler to a hotter object if nothing else happens. 

No violation of either physical statement of the second law of thermodynamics has ever been observed in a properly done experiment. We regard the second law as a summary and generalization of experimental fact. A machine that would violate the Kelvin statement of the second law and turn heat completely into work in a cyclic process is called a perpetual motion machine of the second kind. 

Addressing the second question first leads to a critical constraint when thinking about new, more sustainable, technological developments, that is, the universal applicability of the laws of thermodynamics to aU physical, chemical and biological processes. A central and inescapable fact is the inevitability of waste formation. One statement of the second law of thermodynamics says that heat cannot be converted completely into work. Or, in other words, the energy output of work is always less than the energy transformed to accomplish it. A consequence of this is that, even in principle, it is impossible for any real process to proceed without the generation of some sort of waste. 

For a scientist, the primary interest in thermodynamics is in predicting the spontaneous direction of natural processes, chemical or physical, in which by spontaneous we mean those changes that occur irreversibly in the absence of restraining forces—for example, the free expansion of a gas or the vaporization of a hquid above its boiling point. The first law of thermodynamics, which is useful in keeping account of heat and energy balances, makes no distinction between reversible and irreversible processes and makes no statement about the natural direction of a chemical or physical transformation. 

A correlation analysis is a powerful tool used widely in various fields of theoretical and experimental chemistry. Generally, such an analysis, based on a statistically representative mass of data, can lead to reliable relationships that allow us to predict or to estimate important characteristics of still unknown molecular systems or systems unstable for direct experimental measurements. First, this statement concerns structural, thermodynamic, kinetic, and spectroscopic properties. For example, despite the very complex nature of chemical screening in NMR, particularly for heavy nuclei, various incremental schemes accurately predict their chemical shifts, thus providing a structural analysis of new molecular systems. Relationships for the prediction of physical or chemical properties of compounds or even their physiological activity are also well known. 

Moreover, even if this tautological character is accepted, the statement (5.79) apparently lacks validity for any real substance. Indeed, as shown in Sidebar 5.17, it is probable that every real substance has S0 0, and is therefore imperfect in this respect. (The specific case of H20 is described more completely in Sidebar 5.18.) We conclude that statement (5.79) is meaninglessly tautological as well as inapplicable or invalid for every known physical system. Hence, this statement fails to exhibit the rigorous inductive generality that is inherent in other thermodynamic laws. 

In Chap. 1, we introduced the book with a quote from Albert Einstein (Schilpp 1949), which read in part that classical thermodynamics... is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown. An important qualification to this statement is the phrase within the framework of the applicability of its basic concepts. The laws of thermodynamics are based on laboratory-scale experiments. To assume that such laws are applicable to the Universe is a big assumption. However, we have no evidence yet that contradicts this assumption on the scales of problems relevant to life. Moreover, there remain vast cosmological questions with no answers and definitely no understanding of implications even if we knew the answers. For instance, does the proton have a very long but finite radioactive half-life Does the neutrino have a very small but finite mass Is the Universe opened or closed with respect to expansion and gravitational contraction Also, the Universe may not be isolated with respect to matter/energy or it could be isolated and cyclical. 

This formalism can now be applied, as an example, to our specific physical example where G is the Gibbs free energy and n(x) is the mole distribution. The usual statement in thermodynamics that G is an extensive property can be formalized by requiring the functional G[ ] to be homogeneous of the first degree. Say for any positive scalar O one has... 

In the first part of this century, electrochemical research was mainly devoted to the mercury electrode in an aqueous electrolyte solution. A mercury electrode has a number of advantageous properties for electrochemical research its surface can be kept clean, it has a large overpotential for hydrogen evolution and both the interfacial tension and capacitance can be measured. In his famous review [1], D. C. Grahame made the firm statement that Nearly everything one desires to know about the electrical double layer is ascertainable with mercury surfaces if it is ascertainable at all. At that time, electrochemistry was a self-contained field with a natural basis in thermodynamics and chemical kinetics. Meanwhile, the development of quantum mechanics led to considerable progress in solid-state physics and, later, to the understanding of electrostatic and electrodynamic phenomena at metal and semiconductor interfaces. 

Our first five chapters are devoted to this examination we have taken the greatest pains to free the statements of the primary ideas of Thermodynamics from all algebraic complications the calculus is not used in fact we have supposed on the part of the reader no knowledge in mathematics or physics beyond that possessed by the graduate of a good high school. 

Prom the formal macroscopic statement of the second law of thermodynamics, as developed from classical thermodynamics arguments, it is difficult to assign a physical significance to entropy. Ultimately, you must reassure yourself that entropy is defined mathematically, and like enthalpy, can be used to solve problems even though our physical connexion with the property is occasionally less than satisfying. 

According to Primas (1991, p. 163), "the philosophical literature on reductionism is teeming with scientific nonsense," and he quotes, among others, Kemeny and Oppenheim (1956), who said "a great part of classical chemistry has been reduced to atomic physics." Perhaps it was not philosophers who invented this story after all. Almost certainly, Oppenheim and other philosophers of science at the time were familiar with the influential statements of Dirac, Heisenberg, Reichenbach, and Jordan on this issue. " Notoriously, the physicist Dirac (1929, p. 721) said, the underlying laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact applications of these laws lead to equations which are too complicated to be soluble." Less famously, the philosopher of science Reichenbach (1978, p. 129) reiterated that "the problem of physics and chemistry appears finally to have been resolved today it is possible to say that chemistry is part of physics, just as much as thermodynamics or the theory of electricity." These views clearly stuck. For example, in a recent review of quantum electrodynamics (QED), to which Dirac made important contributions, the historian of science Schweber (1997, p. 177) says, "the laws of physics encompass in principle the phenomena and the laws of chemistry."... 

In Chapter 1 we introduced tliermodyiiainies as the central macroscopic physical theory that allows us to deal with thermophysical phenomena in confined fluids. However, as we mentioned at the outset, thermodynamics as such does not permit us to draw any quantitative conclusions about a specific physical system without taking recourse to additional sources of information such as experimental data or (empirical) equations of state based on these data. Instead thermodynamics makes rigorous. statements about the relation among its key quantitic s sucli as tcanperature, internal energy, entropy, heat, and work. It does not permit one to calcrdate any numbers for these quantities. 

Let us spend a few minutes considering what minimum physical content is necessarily involved and must be present in any formulation of the laws of thermodynamics. In the course of this, a number of conventional statements of the laws will crop up. 

Whittaker (1951) identifies laws of physics that have permanent and absolute character as Postulates of Impotence. They are negative statements in the sense they posit that something is impossible. It is well known that the laws of thermodynamics are qualitative assertions of what cannot happen. Whittaker successfully argues that the fundamental laws of electromagnetism, relativity, and quantum mechanics are also based on negative statements. He then claims, The postulates of this kind already known have proved so fertile in yielding positive results indeed very large part... 

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