SYSTEMS OF COMPUTER MATHEMATICS AND SOME QUESTIONS OF TEACHING THERMODYNAMICS AND STATISTICAL PHYSICS
DOI: 10.23951/1609-624X-2017-4-89-95
Computer algebra systems are now ubiquitous in all areas of science and engineering. Mathcad is one of the most successeful and widely used mathematical package. The capabilities of the mathematical package Mathcad are used to compute approximate solutions of different kinds of equations from statistical physics and thermodynamics. Solved numerically the equations in which the unknown enters under the integral sign. The presented examples are of independent interest to the students and teachers that use numerical methods. The equation of heat balance is difficult to solve when the specific heat depends on temperature and this dependence is given in the form of a table. Spline interpolation is applied to solve the heat balance equation in such a case. Debay’s theory of heat capacity of crystals well describes the temperature dependence of specific heat capacities of some substances. The Debay’s theory is used to numerically solve the heat balance equation for aluminium and copper. Distribution Fermi–Dirac can be used for calculations if the chemical potential is known. The chemical potential implicitly depends on the concentration and temperature. It is shown how to numerically calculate the chemical potential. Shows how to solve numerically and graphically an equation arising in the derivation of the Wien’s shift law. With the help of Planck’s formula determines the temperature of the stars having a maximum proportion of radiation in the visible range. Provides the problems associated with the Maxwell distribution. Without the Boltzmann distribution the pressure of the isothermal atmosphere at a specified altitude is calculated.
Keywords: computer mathematics systems, spline interpolation, numerical solution of equations, statistical distribution
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Issue: 4, 2017
Series of issue: Issue 4
Rubric: ISSUES OF NATURAL-SCIENTIFIC EDUCATION
Pages: 89 — 95
Downloads: 1257