The Nature of a Physical Quantity

A physical quantity is composed of a dimensionless number and the unit. If a car is moving with 90kmh, as referred to commonly in newspapers, then 90 is the dimensionless number and kmh is the unit. Here we must take care because in the present case kmh is an abbreviation for a composed unit. In particular, kmh does not mean km h, but it means km h and what is given in the newspapers is not just wrong, but it is highly misleading. Even in the sciences, we have sometimes such a situation. For example, the unit for the pressure is Pa, i.e., Pascal, in honor to Blaise PascalJ On the other hand. Pa may be understood as Peta years, with P for 10 and a as the abbreviation for year, from the Latin word annum. 

Further, in the older literature, often the pressure is expressed in mm Hg, which is in fact not a length, but the pressure that exerts a column of mercury with the specified length (normalized at 0 °C). Therefore, also in the scientific literature, there are pitfalls concerning units. 

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In a more recent development, it has been shown that the "equally likely" hypothesis of Edwards is not essential for the definition of a temperature-like quantity and the much weaker condition of factorizability of distributions (the density of states factorization discussed in the previous section, e.g.) is sufficient [5-7]. The necessary conditions for being able to define a temperature-like variable and a statistical ensemble based on this variable are (I) the existence of a physical quantity that is conserved by the natural dynamics of the system (in thermal systems energy is conserved but in dissipative granular media, it is not) and (II) the frequency of finding different states with the same value of the conserved quantity is factorizable The latter condition implies that if one... 

The remaining errors in the data are usually described as random, their properties ultimately attributable to the nature of our physical world. Random errors do not lend themselves easily to quantitative correction. However, certain aspects of random error exhibit a consistency of behavior in repeated trials under the same experimental conditions, which allows more probable values of the data elements to be obtained by averaging processes. The behavior of random phenomena is common to all experimental data and has given rise to the well-known branch of mathematical analysis known as statistics. Statistical quantities, unfortunately, cannot be assigned definite values. They can only be discussed in terms of probabilities. Because (random) uncertainties exist in all experimentally measured quantities, a restoration with all the possible constraints applied cannot yield an exact solution. The best that may be obtained in practice is the solution that is most probable. Actually, whether an error is classified as systematic or random depends on the extent of our knowledge of the data and the influences on them. All unaccounted errors are generally classified as part of the random component. Further knowledge determines many errors to be systematic that were previously classified as random. 

A deeper insight into the physical nature of the process. By representing experimental data in a dimensionless form, physical states (e.g. turbulent or laminar flow range, suspension state, heat transfer by natural or by forced convection, and so on) can be delimited from each other and the limits quantified. In this manner, the domain of individual physical quantities also becomes apparent. 

Exponential decay — Many natural processes can be described by the differential equation dx/ df = -Ax. This means that the temporal decay of a physical quantity x is proportional to its absolute value. The solution of this differential equation is x = x0 e Xt for Xo being the starting value of x. The constant A is called the decay constant and its reciprocal value r = A-1 is called - time constant because it has the unit of time, and it is the time necessary for a decay of x to x0e-1 = 0.367... xxq. Typi-... 

Whenever (here is concentration difference of a physical quantity in a medium, nature lends to equalize tilings by forcing a flow from the lilgh to the low concentration region. 

We define quantitative scientific knowledge as the combination of numerical data and formulas. A quantity can be a geometrical quantity like area or volume, or a physical quantity like mass or viscosity. A geometrical quantity is a variable which depends on the geometrical shape under consideration. Physical quantities can be categorised into constant properties and variables. Physical constants are the universal constants of nature, such as Boltzmann s constant (k = 1.380658 10-23/A-1). Physical properties are quantities which hold different values for different substances (or elements) in different states, for example, the Critical Volume (m3 mo/-1) 72.5 10-6 of Ammonia. The physical constants and physical properties are held in a database. Physical variables (sometimes called state variables) are independent variables which describe the state of a physical system, such as temperature (T) or pressure (P). The variables (including geometric values) are either specified by a user or computed by the system. 

Recently the question of the number of basic units necessary to describe any physical system has been revisited and reviewed [26], In the Gaussian system, three basic dimensions are still necessary and sufficient to express the dimension of any physical quantity. These correspond to space (L), time (T), and matter (M). The number of units do not depend on the number and the nature of fundamental interactions in world. For example the basic units would be consistent with a world without gravity. Even electric and magnetic phenomena can be expressed based on space, time, and matter. In 1870, Stoney, associated another meaning to the fundamental units ... 

The central role of the concept of polarity in chemistry arises from the electrical nature of matter. In the context of solution chemistry, solvent polarity is the ability of a solvent to stabilize (by solvation) charges or dipoles. " We have already seen that the physical quantities e (dielectric constant) and p (dipole moment) are quantitative measures of properties that must be related to the qualitative concept of... 

The choice of physical variables to be included in the dimensional analysis must be based on an understanding of the nature of the phenomenon being studied although, on occasions there may be some doubt as to whether a particular quantity is relevant or not. 

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