Laws of experimentation

When contemplating the choice of technique one must keep in mind two further, highly relevant. Laws of Experimentation ... 

In these two cases, the results obtained in Sect. 5.2.2 can be applied. However, it must be emphasized that linearization changes the distribution law of experimental errors and, thus, could induce serious errors in parameter estimation, mainly when the scattering of experimental points is important. 

With the reference block method the distance law of a model reflector is established experimentally prior to each ultrasonic test. The reference reflectors, mostly bore holes, are drilled into the reference block at different distances, e.g. ASME block. Prior to the test, the reference reflectors are scanned, and their maximised echo amplitudes are marked on the screen of the flaw detector. Finally all amplitude points are connected by a curve. This Distance Amplitude Curve (DAC) serves as the registration level and exactly shows the amplitude-over-distance behaviour" of the reference reflector for the probe in use. Also the individual characteristics of the material are automatically considered. However, this curve may only be applied for defect evaluation, in case the reference block and the test object are made of the same material and have undergone the same heat treatment. As with the DGS-Method, the value of any defect evaluation does not consider the shape and orientation of the defect. The reference block method is safe and easy to apply, and the operator need not to have a deep understanding about the theory of distance laws. 

It is important to recognize that thennodynamic laws are generalizations of experimental observations on systems of macroscopic size for such bulk systems the equations are exact (at least within the limits of the best experimental precision). The validity and applicability of the relations are independent of the correchiess of any model of molecular behaviour adduced to explain them. Moreover, the usefiilness of thennodynamic relations depends cmcially on measurability, unless an experimenter can keep the constraints on a system and its surroundings under control, the measurements may be worthless. 

It is a universal experimental observation, i.e. a law of nature , that the equations of state of systems 1 and 2 are then coupled as if the wall separating them were diathemiic rather than adiabatic. In other words, there is a relation... 

One may now consider how changes can be made in a system across an adiabatic wall. The first law of thermodynamics can now be stated as another generalization of experimental observation, but in an unfamiliar form the M/ork required to transform an adiabatic (thermally insulated) system, from a completely specified initial state to a completely specifiedfinal state is independent of the source of the work (mechanical, electrical, etc.) and independent of the nature of the adiabatic path. This is exactly what Joule observed the same amount of work, mechanical or electrical, was always required to bring an adiabatically enclosed volume of water from one temperature 0 to another 02. 

As we have seen, the third law of thermodynamics is closely tied to a statistical view of entropy. It is hard to discuss its implications from the exclusively macroscopic view of classical themiodynamics, but the problems become almost trivial when the molecular view of statistical themiodynamics is introduced. Guggenlieim (1949) has noted that the usefiihiess of a molecular view is not unique to the situation of substances at low temperatures, that there are other limiting situations where molecular ideas are helpfid in interpreting general experimental results ... 

A theoretical basis for the law of corresponding states can be demonstrated for substances with the same intemiolecular potential energy fimction but with different parameters for each substance. Conversely, the experimental verification of the law implies that the underlying intemiolecular potentials are essentially similar in fomi and can be transfomied from substance to substance by scaling the potential energy parameters. The potentials are then said to be confomial. There are two main assumptions in the derivation ... 

As in tire one-fluid case, the experimental sums are in good agreement with the law of the rectilinear diameter, but the experimental differences fail to give a parabolic shape to tlie coexistence curve. 

In 1945 Guggeitiieim [10], as part of an extensive diseussion of the law of eorresponding states, showed that, when plotted as redueed temperature versus redueed density p, all the eoexistenee-eurve measurements on tlnee inert gases (Ar, Kr, Xe) fell on a single eurve, and that Ne, N2, O2, CO and CH also fit the same eurve very elosely. Moreover he either rediseovered or re-emphasized the faet that the eurve was unequivoeally eubie (i.e. p = 1/3) over tire entire range of experimental temperatures, writing for p... 

The phenomenon of thermal transpiration was discovered by Osborne Reynolds [82], who gave a clear and detailed description of his experiments, together with a theoretical analysis, in a long memoir read before the Royal Society in February of 1879. He experimented with porous plates of stucco, ceramic and meerschaum and, in the absence of pressure gradients, found that gas passes through the plates from the colder to the hotter side. His experimental findings were summarized in the following "laws" of thermal transpiration. 

Most observations in chemistry come from ex periments If we do enough experiments we may see a pattern running through our observations A /aw is a mathematical (the law of gravity) or verbal (the law of diminishing returns) description of that pattern Establishing a law can lead to the framing of a rule that lets us predict the results of future experiments This IS what the 1870 version of Markovnikov s rule is a statement based on experimental observations that has predictive value... 

Classical and Quantum Mechanics. At the beginning of the twentieth century, a revolution was brewing in the world of physics. For hundreds of years, the Newtonian laws of mechanics had satisfactorily provided explanations and supported experimental observations in the physical sciences. However, the experimentaUsts of the nineteenth century had begun delving into the world of matter at an atomic level. This led to unsatisfactory explanations of the observed patterns of behavior of electricity, light, and matter, and it was these inconsistencies which led Bohr, Compton, deBroghe, Einstein, Planck, and Schrn dinger to seek a new order, another level of theory, ie, quantum theory. 

This has the advantage that the expressions for the adsotbed-phase concentration ate simple and expHcit, and, as in the Langmuir expression, the effect of competition between sorbates is accounted for. However, the expression does not reduce to Henry s law in the low concentration limit and therefore violates the requirements of thermodynamic consistency. Whereas it may be useful as a basis for the correlation of experimental data, it should be treated with caution and should not be used as a basis for extrapolation beyond the experimental range. 

Mechanisms. Mechanism is a technical term, referring to a detailed, microscopic description of a chemical transformation. Although it falls far short of a complete dynamical description of a reaction at the atomic level, a mechanism has been the most information available. In particular, a mechanism for a reaction is sufficient to predict the macroscopic rate law of the reaction. This deductive process is vaUd only in one direction, ie, an unlimited number of mechanisms are consistent with any measured rate law. A successful kinetic study, therefore, postulates a mechanism, derives the rate law, and demonstrates that the rate law is sufficient to explain experimental data over some range of conditions. New data may be discovered later that prove inconsistent with the assumed rate law and require that a new mechanism be postulated. Mechanisms state, in particular, what molecules actually react in an elementary step and what products these produce. An overall chemical equation may involve a variety of intermediates, and the mechanism specifies those intermediates. For the overall equation... 

Both ultrasonic and radiographic techniques have shown appHcations which ate useful in determining residual stresses (27,28,33,34). Ultrasonic techniques use the acoustoelastic effect where the ultrasonic wave velocity changes with stress. The x-ray diffraction (xrd) method uses Bragg s law of diffraction of crystallographic planes to experimentally determine the strain in a material. The result is used to calculate the stress. As of this writing, whereas xrd equipment has been developed to where the technique may be conveniently appHed in the field, convenient ultrasonic stress measurement equipment has not. This latter technique has shown an abiHty to differentiate between stress reHeved and nonstress reHeved welds in laboratory experiments. 

Fundamental Property Relation. The fundamental property relation, which embodies the first and second laws of thermodynamics, can be expressed as a semiempifical equation containing physical parameters and one or more constants of integration. AH of these may be adjusted to fit experimental data. The Clausius-Clapeyron equation is an example of this type of relation (1—3). 

The ideal gas law is an example of a correlating expression that comes direcdy from experimental observations, but has theoretical significance. Despite its simplicity, the ideal gas law is an excellent estimation tool. Often, it is the first approximation in systems involving real gases of all types. Unfortunately for Hquids and soHds no laws of such general utility are available. 

Our discussion to this point has been confined to those areas in which the governing laws are well known. However, in many areas, information on the governing laws is lacking. Interest in the application of statistical methods to all types of problems has grown rapidly since World War II. Broadly speaking, statistical methods may be of use whenever conclusions are to be drawn or decisions made on the basis of experimental evidence. Since statistics could be defined as the technology of the scientific method, it is primarily concerned with the first two aspec ts of the method, namely, the performance of experiments and the drawing of conclusions from experiments. Traditionally the field is divided into two areas ... 

Nienow and Conti (1978) developed a model of partiele abrasion at high solids eoneentration based on Rittinger s law of eomminution. When tested experimentally using eopper sulphate and niekel ammonium sulphate erystals in two non-solvent liquids, measured abrasion rates were eonsistent with a seeond-order dependenee of eoneentration as predieted (Figure 5.12). 

In a similar way, computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws of physics. It allows chemists to study chemical phenomena by running calculations on computers rather than by examining reactions and compounds experimentally. Some methods can be used to model not only stable molecules, but also short-lived, unstable intermediates and even transition states. In this way, they can provide information about molecules and reactions which is impossible to obtain through observation. Computational chemistry is therefore both an independent research area and a vital adjunct to experimental studies. 

Ab initio methods, unlike either molecular mechanics or semi-empirical methods, use no experimental parameters in their computations. Instead, their computations are based solely on the laws of quantum mechanics—the first principles referred to in the name ah initio—and on the values of a small number of physical constants ... 

The laws of electrolysis were discovered by Michael Faraday, perhaps the most talented experimental scientist of the nineteenth century. 

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