Theory absolute speeds

If a hypothesis successfully passes many tests, it becomes known as a theory. A theory is a tested explanation of basic natural phenomena. An example is the molecnlar theory of gases— the theory that all gases are composed of very small particles called molecules. This theory has withstood many tests and has been fruit-fnl in snggesting many experiments. Note that we cannot prove a theory absolutely. It is always possible that further experiments will show the theory to be limited or that someone will develop a better theory. For example, the physics of the motion of objects devised by Isaac Newton withstood experimental tests for more than two centnries, nntil physicists discovered that the equations do not hold for objects moving near the speed of light. Later physicists showed that very small objects also do not follow Newton s eqnations. Both discoveries resulted in revolutionary developments in physics. The first led to the theory of relativity the second, to quantum mechanics, which has had an immense impact on chemistry. 

Following collision theory, a model of the bimolecular reaction, called the theory of activated complexs or the theory of absolute speeds, was estabhshed in 1938 by Eyring and Polanyi respectively. 

In theory, since the absolute water vapor content of air reduces as the temperature sinks or the altitude rises, the volume of precipitation should decline. Yet the opposite is the case, particularly in mountainous regions in the temperate latitudes here the annual volumes of precipitation generally tend to rise with the altitude. This is the result, on the one hand, of higher wind speeds at higher altitudes, which cause a relatively large shift in humid air masses. On the other hand, precipitation occurs more frequently and often at a much greater intensity. 

One particularly efficient alternative is to develop SARs not with experimental molecular properties, but with predicted ones. Thus, if the drug company database is augmented with predicted values, and a SAR on predicted values proves useful based on data for compounds already assayed, potential new compounds can be examined in a purely computational fashion to evaluate whether they should be priority targets for synthesis. In 1998, Beck et al. (1998) optimized the geometries of a database of 53000 compounds with AMI in 14 hours on a 128-processor Origin 2000 computer. Such speed is presently possible only for semiempirical levels of theory. Once the geometries and wave functions are in hand, it is straightforward (and typically much faster) to compute a very wide variety of molecular properties in order to survey possible SARs. Note that for the SAR to be useful, the absolute values of the computed properties do not necessarily need to be accurate - only their variation relative to their activity is important. 

The rate at which the momentum transfer takes place is dependent on the rate at which the molecules move across the fluid layers. In a gas, the molecules would move about with some average speed proportional to the square root of the absolute temperature since, in the kinetic theory of gases, we identify temperature with the mean kinetic energy of a molecule. The faster the molecules move, the more momentum they will transport. Hence we should expect the viscosity of a gas to be approximately proportional to the square root of temperature, and this expectation is corroborated fairly well by experiment. The viscosities of some typical fluids are given in Appendix A. 

While, even accepting discrepancies by a factor of O 2, the fulfillment of Eqs. (l)-(7) does not constitute proof of Planck-power input, it at least seems suggestive. Could Planck-power input, if it exists, be a classical process independent of quantum effects, if not absolutely then at least via opposing quantum effects canceling out, as h cancels out in the division Ppianck = Planck / Planck Note that perhaps similar canceling out obtains with respect to the Planck speed /pianck/f Planck = c c is the fundamental speed in the classical (nonquantum) theories of Special and General Relativity. 

A fundamental principle of science is that simpler models are more useful than complex ones—as long as they explain the data. You can certainly appreciate the usefulness of the kinetic-molecular theory. With simple postulates, it explains the behavior of the ideal gases in terms of particles acting like infinitesimal billiard balls, moving at speeds governed by the absolute temperature, and experiencing only perfectly elastic collisions. 

Collision frequency Z, the frequency with which the reactant molecules collide, depends on temperature. As you will see, however, this dependence of colhsion frequency on temperature does not explain why reaction rates usually change greatly with small temperature increases. You can easily explain why the collision frequency depends on temperature. As the temperature rises, the gas molecules move faster and therefore collide more frequently. Thus, collision frequency is proportional to the root-mean-square (rms) molecular speed, which in turn is proportional to the square root of the absolute temperature, according to the kinetic theory of gases. From kinetic theory, one can show that at 25°C, a 10°C rise in temperature increases the colhsion frequency by about 2%. If you were to assume that each collision of reactant molecules resulted in reaction, you would conclude that the rate would increase... 

It is at present too much to expect that the absolute magnitude of friction can be predicted to a reasonable degree of accuracy from any available theories. On the other hand, a good measure of the success of a theory may be obtained from the extent to which friction varies with speed. The essential feature of the details of the model may thereby be verified. The reason for this statement is that the absolute magnitude of friction depends strongly upon the absolute values of the less tractable parameters viz. strength of adhesion and real area of contact the variation of friction with speed is strongly related only to the more tractable viscoelastic properties,... 

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