Law-like statements

There have been a number of proposals to deal with these problems. One suggestion is to argue that the law-like statements that constitute the body of our theories ought to be taken as not literally true, as false. Another is to take these law-like assertions as intended to apply not to the real systems in the world at all. Rather, they are supposed to be descriptive of the behavior only of idealized entities, of models. Then, it is su ested, they apply to the real world indirectly by means of some resemblance to limited degrees and in limited aspects of these models to the real systems of the world. 

Coulomb s law the statement that like charges repel and unlike charges attract along with the equations for predicting the magnitude of those interactions coupled cluster (CC) a correlated ah initio method... 

Let us now attempt to re-express the Gibbs criterion of equilibrium in alternative analytical and graphical forms that are more closely related to Clausius-like statements of the second law. For this purpose, we write the constrained entropy function S in terms of its... 

Note that the stoichiometric coefficients in a balanced chemical equation like eq. (2.5) bear no necessary relationship to the orders that appear in the empirical (i.e., experimentally derived) rate law. This statement becomes obvious if one considers that the chemical equation can be multiplied on both sides by any arbitrary number and remain an accurate representation of the stoichiometry even though all the coefficients will change. However, the orders for the new reaction will remain the same as they were for the old one. There are cases in which the rate law depends only on the reactant concentrations and in which the orders of the reactants equal their molecularity. A reaction in which the order of each reactant is equal to its molecularity is said to obey the Law of Mass Action or to behave according to mass action kinetics. 

In some cases, a series of similar observations leads to the development of a scientific law, a brief statanent that summarizes past observations and predicts future ones. Lavoisier summarized his observations on combustion with the law of conservation of mass, which states, In a chonical reaction, matter is neither created nor destroyed. This statement summarized his observations on chanical reactions and predicted the outcome of future observations on reactions. Laws, like hypotheses, are also subject to experiments, which can support them or prove than wrong. 

Like the engine-based statements, Caratheodory s statement invokes limitations. From a given thermodynamic state of the system, there are states that cannot be reached from the initial state by way of any adiabatic process. We will show that this statement is consistent with the Kelvin-Planck statement of the Second Law. 

Introduction of the reptation concept by De Gennes [43] led to further essential progress. Proceeding from the notion of a reptile-like motion of the polymer chains within a tube of fixed obstacles, De Gennes [43-45], Doi [46,47] and Edwards [48] were able to confirm Bueche s 3.4-power-law for polymer melts and concentrated polymer solution. This concept has the disadvantage that it is valid only for homogeneous solutions and no statements about flow behaviour at finite shear rates are analysed. 

Besides its problems in undermining putative macromolecular explanations of (PS), (G) and what (G) explains, antireductionism faces some problems in substantiating its claims that (PS) explains (G) and (G) explains individual cases of genetic recombination. The problems, of course, stem from the fact that neither (PS) nor (G) are laws, and therefore an account is owing of how statements like these can explain. This, in fact, is a problem that any revision of a thesis of reductionism must come to grips with as well. So, perhaps we should turn to this problem directly, and then reformulate and reassess both reductionism and antireductionism as explanatory theses in its light. 

In the era when these statements were made they were quite bold, if not radical, and likely to have been received with much indifference and perhaps opposition, especially since the statements were made by a woman. In 1928, only 8 years had elapsed since the Nineteenth Amendment to the US Constitution had, after intense debate, become law and allowed women to vote. The U S economy was doing well and jobs were plentiful. Although it undoubtedly existed, pollution was not viewed as a problem by the general population or the federal government. As such, very few federal laws or regulatory authorities existed that regulated the development and marketing of commercial industrial chemicals, pesticides, or pharmaceutical substances to protect human health and the environment from risks posed by such substances. 

It was the principal genius of J. W. Gibbs (Sidebar 5.1) to recognize how the Clausius statement could be recast in a form that made reference only to the analytical properties of individual equilibrium states. The essence of the Clausius statement is that an isolated system, in evolving toward a state of thermodynamic equilibrium, undergoes a steady increase in the value of the entropy function. Gibbs recognized that, as a consequence of this increase, the entropy function in the eventual equilibrium state must have the character of a mathematical maximum. As a consequence, this extremal character of the entropy function makes possible an analytical characterization of the second law, expressible entirely in terms of state properties of the individual equilibrium state, without reference to cycles, processes, perpetual motion machines, and the like. 

For two polar molecules arranged as in Fig. la, the attractions between opposite charges exceed the repulsions between like charges. This statement may (if necessary) be confirmed by a simple Coulombs s Law calculation based on the bond-lengths and van der Waals contact specified in the diagram. The total force will be the difference between attraction and repulsion ... 

Theories perform several functions in science. They help us to organize observations, which I like to call their filing cabinet or mapping function. Instead of memorizing thousands of separate observations, you memorize a theory from which you can predict these observations, which constitutes quite a saving of work. Theories also make predictions about where we should look for other data that may be of value to us. But they are never quite final. A theory is always subject to test as new predictions evolve from it. This applies even to so-called scientific laws. A scientific law is simply a theory that has worked so exceptionally well in untold thousands of trials that we have taken the human step of believing that it is a true statement about the ultimate nature of the universe, rather than a theory or concept that we have about it. The so-called law of gravity, for example, is a scientific theory about the effect... 

In the course of a change in the German criminal law at the end of the 70s, the duty to make entries in the record of the proceedings was removed for reasons of economy for all courts higher than the County Courts. What appears now in German trial records is something like The witness made statements on the subject or The accused made a declaration . The substance of what was said cannot be found there and it can no longer be proven by documentation when the court uses statements incorrectly.565... 

The existence of an energy balance is not sufficient to answer all questions about a chemical reaction. Does a given reaction take place at all If so, to what extent does it proceed Questions relating to the processes and extent of chemical reactions require the introduction of some new thermodynamic functions which, like E and //, are properties of the state of the system. These new functions are entropy, S, and Gibbs free energy, G. In order to answer these and other questions, a mathematical statement of the second law of thermodynamics is required ... 

Gas molecules do not actually bounce off the wall of a container (or your skin) as if it were a uniform massive structure, the way we sketched it in Figure 7.2 they collide with individual atoms at the wall surface, which are also moving because of vibrations. If the temperature of the wall and the gas are the same, on average the gas kinetic energy is as likely to increase or decrease as a result of any single collision. Thus a more accurate statement of the assumption required to derive the ideal gas law is that the walls and gas molecules are at the same temperature, so there is no average energy flow between the two. 

---