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Geometric analysis of thermodynamic ...

Carnegie Mellon University.

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Geometric analysis of thermodynamic equilibrium processes.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Geometric analysis of thermodynamic equilibrium processes./
Author:	Xu, Yuan.
Description:	149 p.
Notes:	Source: Dissertation Abstracts International, Volume: 69-04, Section: B, page: 2488.
Contained By:	Dissertation Abstracts International69-04B.
Subject:	Engineering, Chemical. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoeng/servlet/advanced?query=3311768
ISBN:	9780549597575

Geometric analysis of thermodynamic equilibrium processes.
Xu, Yuan.

Geometric analysis of thermodynamic equilibrium processes. - 149 p.

Source: Dissertation Abstracts International, Volume: 69-04, Section: B, page: 2488.

Thesis (Ph.D.)--Carnegie Mellon University, 2008.

We introduce a method for the analysis of the asymptotic behavior of thermodynamic equilibrium processes from a geometric viewpoint. In many of the previous studies the thermodynamic equilibrium conditions were enforced approximately or incorrectly. In this work, a geometric interpretation is given for the thermodynamics equilibrium conditions by proving that the global minimum of the Gibbs free energy is located on the convex hull of the molar Gibbs energy function. This geometric equivalence is extended to the general equilibrium defined by the maximization of entropy and the chemical phase equilibrium. The convex hulls for the thermodynamic functions are shown to be C1-smooth. As a result, the boundary between the single phase region and the multiple ones is also smooth. This property can be used to check the phase diagrams generated from numerical calculation. A phase number function defined on the domain of the convex hull is shown to be lower semi-continuous and is used to investigate the properties of the phase regions. In particular, the properties of the two phase regions are used in the stability analysis of the isothermal isobaric flash. Its dynamics are given a clear geometric explanation and it is shown to converge to a steady state. This analysis method is extended to the adiabatic flash and the reactive flash with equimolar reactions. Finally, the uniqueness of the steady state is analyzed for different flash processes.

ISBN: 9780549597575Subjects--Topical Terms:

1018531
Engineering, Chemical.

Geometric analysis of thermodynamic equilibrium processes.
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008 100719s2008 ||||||||||||||||| ||eng d
020 $a 9780549597575
035 $a (UMI)AAI3311768
035 $a AAI3311768
040 $a UMI $c UMI
100 1 $a Xu, Yuan. $3 1029221
245 1 0 $a Geometric analysis of thermodynamic equilibrium processes.
300 $a 149 p.
500 $a Source: Dissertation Abstracts International, Volume: 69-04, Section: B, page: 2488.
502 $a Thesis (Ph.D.)--Carnegie Mellon University, 2008.
520 $a We introduce a method for the analysis of the asymptotic behavior of thermodynamic equilibrium processes from a geometric viewpoint. In many of the previous studies the thermodynamic equilibrium conditions were enforced approximately or incorrectly. In this work, a geometric interpretation is given for the thermodynamics equilibrium conditions by proving that the global minimum of the Gibbs free energy is located on the convex hull of the molar Gibbs energy function. This geometric equivalence is extended to the general equilibrium defined by the maximization of entropy and the chemical phase equilibrium. The convex hulls for the thermodynamic functions are shown to be C1-smooth. As a result, the boundary between the single phase region and the multiple ones is also smooth. This property can be used to check the phase diagrams generated from numerical calculation. A phase number function defined on the domain of the convex hull is shown to be lower semi-continuous and is used to investigate the properties of the phase regions. In particular, the properties of the two phase regions are used in the stability analysis of the isothermal isobaric flash. Its dynamics are given a clear geometric explanation and it is shown to converge to a steady state. This analysis method is extended to the adiabatic flash and the reactive flash with equimolar reactions. Finally, the uniqueness of the steady state is analyzed for different flash processes.
590 $a School code: 0041.
650 4 $a Engineering, Chemical. $3 1018531
650 4 $a Engineering, Mechanical. $3 783786
650 4 $a Mathematics. $3 515831
690 $a 0405
690 $a 0542
690 $a 0548
710 2 $a Carnegie Mellon University. $3 1018096
773 0 $t Dissertation Abstracts International $g 69-04B.
790 $a 0041
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoeng/servlet/advanced?query=3311768