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- Title
Дослідження похідних термодинамічних функцій для кривої ДжоуляТомсона на основі рівняння стану Ван-дер-Ваальса.
- Authors
Троценко, О. В.
- Abstract
The Joule-Thomson effect is widely used in the design of refrigeration and cryogenic installations. Interest in it does not weaken, despite the one and a half month period from the day of its opening. This is explained by the fact that the so-called inversion curve of the throttle effect in thermodynamics is ideal. This circumstance contributes to a deeper study of the inversion curve when developing the equations of state of real gases. It should also be taken into account that there are no studies on the peculiarities of the inversion curve as a mathematical object. For example, no publications were found that studied derivatives on this curve. The purpose of the work is to establish the values and carry out an analysis of the features of a number of first and second derivatives of thermodynamic functions on the Joule-Thomson line. Two approaches are used: in the first one, an analytical description of inversion curves in π,φ- and π,τ-coordinates is used, in the second one, modern means of symbolic calculations are used. Analytical dependences were obtained for the parameters of the Joule-Thomson curve when using the given van der Waals equation of state in a dimensionless form. This choice is due to the fact that, firstly, the equation does not depend on the type of pure substance; secondly, for this equation, as further studies show, all solutions can be obtained analytically thanks to the modern capabilities of computing technology. In addition, no results of symbolic calculations for the inversion curve based on the van der Waals equation of state were found in the literature. Graphical dependences for first- and second-order derivatives on the inversion curve are given and analyzed. It was concluded that the studied derivatives are monotonic functions of the given temperature. It was established that these derivatives can have extremum points and infinite values only at the upper inversion temperature. The use of general thermodynamic relations to determine the mixed derivative of the second order on the inversion curve is presented.
- Subjects
JOULE-Thomson effect; THERMODYNAMIC functions; REAL gases; TEMPERATURE inversions; MONOTONIC functions; EQUATIONS of state; CURVES; SUPERCONDUCTING magnets
- Publication
Refrigeration Engineering & Technology, 2023, Vol 59, Issue 1, p57
- ISSN
0453-8307
- Publication type
Article
- DOI
10.15673/ret.v59i1.2613