Invariance of the total charge

Invariance of the Total Charge Fundamental and Less Fundamental Invariances... 

Invariance with Respect to Permutation of Identical Particles (Fermions and Bosons) Invariance of the Total Charge Fundamental and Less Fundamental Invariances... 

Certain expenses are always present in an industrial plant whether or not the manufacturing process is in operation. Costs that are invariant with the amount of production are designated as fixed costs or fixed charges. These include costs for depreciation, local property taxes, insurance, and rent. Expenses of this type are a direct function of the capital investment. As a rough approximation, these charges amount to about 10 to 20 percent of the total product cost. 

Any increase in the concentration of one anion is accompanied either by a corresponding decrease in other anions or by an increase in one or more cations or both, so total electrical neutrality is invariably maintained. Similarly, any decrease in the concentration of anions involves either a corresponding increase in other anions, or a decrease in cations, or both. In the case of polyvalent ions (e.g., Ca or Mg ), it is important to distinguish between the substance concentration of the ion itself and the concentration of the ion charge. Thus although the concentration of total calcium ions in normal plasma is 2.5 mmol/L> the concentration of the total calcium ion charge is 5.0 mmol/L (also called 5 mil-liequivalents per liter [mEq/L]). This law of electrical neutrality should not be confused with acid-base neutrality (pH = 7.0, where the activity of H" " equals the activity of OH"). 

To conclude this section let us note that already, with this very simple model, we find a variety of behaviors. There is a clear effect of the asymmetry of the ions. We have obtained a simple description of the role of the major constituents of the phenomena—coulombic interaction, ideal entropy, and specific interaction. In the Lie group invariant (78) Coulombic attraction leads to the term -cr /2. Ideal entropy yields a contribution proportional to the kinetic pressure 2 g +g ) and the specific part yields a contribution which retains the bilinear form a g +a g g + a g. At high charge densities the asymptotic behavior is determined by the opposition of the coulombic and specific non-coulombic contributions. At low charge densities the entropic contribution is important and, in the case of a totally symmetric electrolyte, the effect of the specific non-coulombic interaction is cancelled so that the behavior of the system is determined by coulombic and entropic contributions. 

However, when distinguished from the former case, the quantum description also allows degenerate states of the molecule. In each of the states of the degenerate term or in their linear combinations, the charge distribution is not invariant with respect to all the operations of the assumed symmetry of the molecule. Therefore all the conclusions based on the assumption of a totally symmetric charge distribution in the case of degeneracy become invalid. 

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