Calculation with Physical Quantities Problems and Solutions

4 Calculation with Physical Quantities Problems and Solutions 

In the begiiming of this chapter, we noted that Mathcad is not just for mathematical applications only but for physical applications also (see Figs. 6.5 and 6.8). Frequently, the real physical calculations, i.e. where almost all values have units 

Comment. We tell below how to simplify and automate the unit choice from the offered list by interface elements Controls and Web Controls changing the operators of the type variable = quantity unit to more convenient. 

What are the reasons for imperfect use of Mathcad capabilities The first reason is, of course, that some users do not know about such useful Mathcad tool as built-in constants of physical quantities. The users apply techniques in Mathcad, in physical and mathematical programs, based spreadsheet experience or even computer programming (such as C++, Fortran, etc.). Such non-physical languages where the 

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The first type, which includes, for example, the problem of strong explosion or propagation of heat in a medium with nonlinear thermal conductivity [3], is characterized by the fact that the exponents are found from physical considerations, from the conservation laws and their dimensionality. In addition, the exponents turn out to be rational numbers. The task of the calculation is to find the dimensionless functions by integration of ordinary differential equations. After this the problem is completely solved, since the numerical constants are determined by normalizing the solution to the conserved quantity (the total energy released in these examples). 

Before the activity coefficients calculated on the basis of the Debye-Hiickel model can be compared with experiment, there arises a problem similar to one faced in the discussion of ion-solvent interactions (Chapter 2). Thae, it was realized the heat of hydration of an individual ionic species could not he measured because such a measurement would involve the transfer of ions of only one species into a solvent instead of ions of two species with equal and opposite charges. Even if such a transfer were physically possible, it would result in a charged solution and therefore an extra, undesired interaction between the ions and the electrified solution. The only way out was to transfer a neutral electrolyte (an equal number of positive and negative ions) into the solvent, but this meant that one could only measure the heat of interactions of a salt with the solvent and this experimental quantity could not be separated into the individual ionic heats of hydration. 

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