Two Fundamental Laws of Nature

The structure of this text is kept simple in order to make the succession of steps as transparent as possible. The first chapter Two Fundamental Laws of Nature) explains how the first and the second law of thermodynamics can be cast into a useful mathematical form. It also explains different types of work as well as concepts like temperature and entropy. The final result is the differential entropy change expressed through differential changes in internal energy and the various types of work. This is a fundamental relation throughout equilibrium as well as nonequilibrium thermodynamics. The second chapter Thermodynamic Functions),... 

This relation for temperature is often referred to as the zeroth law of thermodynamics. However, in the spirit of Rudolph Clausius, we will view thermodynamics in terms of two fundamental laws of nature that are represented by the first and second laws of thermodynamics. 

Electrons having the same spin strongly repel each other and tend to occupy different regions of space. This is a result of a fundamental law of nature known as the Pauli exclusion principle. It states that total wave functions (including spin) must change their signs on exchange of any pair of electrons in the system. Briefly, this means that if two electrons have the same spin they must have different spatial wave functions (i.e., different orbitals) and if they occupy the same orbital they must have paired spins. The Pauli principle and the so-called Pauli repulsive forces 1 have lar-... 

The finite lifetime of each excited state is the reflection of a fundamental law of nature - tendency towards minimum total energy of a system. The quantum mechanical system tends to occupy the state in which its total energy would be minimal. However, the transition of an atom to the lowest (ground) state depends on many circumstances (first of all, on the sort of excited configuration, on the presence of external fields, on the character of the matter itself - density of gas, vapours or plasma, etc.). There are two main channels of decay of the excited states radiative and radiationless. In the first case the electronic transition from the higher to the lower state is connected with the radiation of one or several quanta of... 

Feb. 20,1844, Vienna, Austria - Sep. 5,1906 in Duino, Austro-Hungarian Empire, now Italy) is justly famous for his invention of statistical mechanics. At different times in his fife he held chairs in theoretical physics at Graz, and in mathematics at Vienna. He also lectured in philosophy. His principal achievement, and the trigger for innumerable vitriolic attacks from the scientific establishment, was his introduction of probability theory into the fundamental laws of physics. This radical program demohshed two centuries of confidence that the fundamental laws of Nature were deterministic. Astonishingly, he also introduced the concept of discrete energy levels more th an thirty years before the development of quantum mechanics. 

For the historians of science our century will probably present a special interest, because in a short period, our view of nature has undergone a fundamental change. If you look back at the beginning of the century, you see that physicists were unanimous to believe that the fundamental laws of nature were deterministic and time-reversible. The two great revolutions of XXth century science, relativity and quantum mechanics, did not seem to change this opinion. 

This difficulty is quite general. Whatever experiments are devised to measure at the same time two conjugate variables, the limit of accuracy always appears to be given by a relation similar to 3 9. This result has been assumed by Heisenberg to be a fundamental law of nature, and is generally known as the imcertainty principle. 

The suggestion in view is that when volume is lost by diffusive mass transfer, the consequent shortening rate along some direction n is controlled by regardless of the spatial variations in other stress components. The nature of the argument advanced is comparable with the one on which the theory of relativity is based At two separate points in a universe, it is not reasonable to suppose that the fundamental laws of behavior will be different at one point from the other. If it is only in respect to some reference frame set up by an observer that point P differs from point Q, one should not expect behavior at P to differ from behavior at Q. It is convenient to use anthropomorphic phrasing If there is nothing intrinsic about point P to tell the material there to behave differently, the material at P will behave in the same way as the material at Q. ... 

With his very fine torsion balance, Coulomb was able to demonstrate that the repulsive force between two small spheres electrified with the same type of electricity is inversely proportional to the square of the distance between the centers of the two spheres. At the time, the electron had not yet been discovered, so the underlying reason for this remained a mystery but Coulomb was able to demonstrate that both repulsion and attraction followed this principle. He was not able to make the quantitative step to show that the force was also directly proportional to the product of the charges, but he did complete some experiments exploring this relationship. As a consequence, the law governing one of the four fundamental forces of nature is named Coulomb s law ... 

Science as a methodical investigation of Nature s capacities evolved from the humble craft tradition. Its goal is to provide the most general and the simplest possible description of the observable character of Nature. In the past the singular concept of science comprised all aspects of intellectual endeavor the arts, the sciences and the crafts. It was Diderot s EncyclopMie ou Dictionnaire Raisonne des Sciences, des Arts et des Metiers of 1751-66 that hrst divided the old science into these three parts. The next split — that between the basic and applied sciences — is barely a century old. Basic science has been described as motivated by the desire to discover connections between natural phenomena, while applied science is the apphcation of the discovered laws of nature for the material benehts of mankind. The boundary between the two is not rigid since experimental observation frequently provides a spur to fundamental discoveries. 

Does a soil-fluid-chemical system behave as an active electrochemical system or a passive electrical conductor under the influence of a DC electric field This is a fundamental question of significant implications. The evaluation criterion that can be used to differentiate the two systems of completely different nature is vested in Faraday s laws of electrolysis, as the transfer of electrons from the electrodes to the system and vice versa in an ideal electrochemical system is invariably associated with chemical reactions obeying Faraday s laws of electrolysis (Antropov, 1972). The two important fundamental laws of electrolysis can be simply expressed as follows (a) the amount of chemical deposition is proportional to the quantity of electric charges flowing through the system in an electrolytic process, and (b) the masses of different species deposited at or dissolved from electrodes by the same quantity of electric charges are directly proportional to their equivalent weights (Crow, 1979). 

The use of hypertext in information science is superior to a traditional linear presentation. It relies on a tree structure. However, it has a serious drawback. Sitting on a branch, we have no idea what that branch represents in the whole diagram, whether it is an important branch or a remote tiny one does it lead further to important parts of the book or it is just a dead end, and so on. At the same time, a glimpse of the TREE shows us that the thick trunk is the most important structure. What do we mean by important At least two criteria may be used. Important for the majority of readers, or important because the material is fundamental for an understanding of the laws of nature. I have chosen the first. For example, relativity theory plays a pivotal role as the foundation of physical sciences, but for the vast majority of chemists its practical importance and impact are much smaller. Should relativity be represented therefore as the base of the trunk, or as a minor branch I have decided to make the second choice not to create the impression that this topic is absolutely necessary for the student. Thus, the trunk of the TREE corresponds to the pragmatic way to study this book. 

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