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Material constants that vary for each type of material are eliminated, in a recast reduced form of a constitutive equation . The reduced variables are defined in terms of critical variables .
The principle originated with the work of Johannes Diderik van der Waals in about 1873[3] when he used the critical temperature and critical pressure to derive a universal property of all fluids that follow the van der Waals equation of state. It predicts a value of
3
/
8
=
0.375
{\displaystyle 3/8=0.375}
that is found to be an overestimate when compared to real gases.
Edward A. Guggenheim used the phrase "Principle of Corresponding States" in an opt-cited paper to describe the phenomenon where different systems have very similar behaviors when near a critical point .[4]
There are many examples of non-ideal gas models which satisfy this theorem, such as the van der Waals model, the Dieterici model, and so on, that can be found on the page on real gases .
Compressibility factor at the critical point [ edit ]
The compressibility factor at the critical point, which is defined as
Z
c
=
P
c
v
c
μ
R
T
c
{\displaystyle Z_{c}={\frac {P_{c}v_{c}\mu }{RT_{c}}}}
, where the subscript
c
{\displaystyle c}
indicates physical quantities measured at the critical point , is predicted to be a constant independent of substance by many equations of state.
The table below for a selection of gases uses the following conventions:
Substance
P
c
{\displaystyle P_{c}}
[Pa ]
T
c
{\displaystyle T_{c}}
[K ]
v
c
{\displaystyle v_{c}}
[m 3 /kg]
Z
c
{\displaystyle Z_{c}}
H 2 O
21.817× 10 6
647.3
3.154× 10 −3
0.23[5]
4 He
0.226× 10 6
5.2
14.43× 10 −3
0.31[5]
He
0.226× 10 6
5.2
14.43× 10 −3
0.30[6]
H 2
1.279× 10 6
33.2
32.3× 10 −3
0.30[6]
Ne
2.73× 10 6
44.5
2.066× 10 −3
0.29[6]
N 2
3.354× 10 6
126.2
3.2154× 10 −3
0.29[6]
Ar
4.861× 10 6
150.7
1.883× 10 −3
0.29[6]
Xe
5.87× 10 6
289.7
0.9049× 10 −3
0.29
O 2
5.014× 10 6
154.8
2.33× 10 −3
0.291
CO 2
7.290× 10 6
304.2
2.17× 10 −3
0.275
SO 2
7.88× 10 6
430.0
1.900× 10 −3
0.275
CH 4
4.58× 10 6
190.7
6.17× 10 −3
0.285
C 3 H 8
4.21× 10 6
370.0
4.425× 10 −3
0.267
See also [ edit ]
References [ edit ]
^ Tester, Jefferson W. & Modell, Michael (1997). Thermodynamics and its applications . Prentice Hall. ISBN 0-13-915356-X .
^ Çengel Y.A.; Boles M.A. (2007). Thermodynamics: An Engineering Approach (Sixth ed.). McGraw Hill. ISBN 9780071257718 . page 141
^ A Four-Parameter Corresponding States Correlation for Fluid Compressibility Factors Archived 2007-03-17 at the Wayback Machine by Walter M. Kalback and Kenneth E. Starling, Chemical Engineering Department, University of Oklahoma .
^ Guggenheim, E. A. (1945-07-01). "The Principle of Corresponding States" . The Journal of Chemical Physics . 13 (7 ): 253–261. doi :10.1063/1.1724033 . ISSN 0021-9606 .
^ a b Goodstein, David (1985) [1975]. "6" [Critical Phenomena and Phase Transitions]. States of Matter (1st ed.). Toronto, Ontario , Canada : General Publishing Company, Ltd. p. 452 . ISBN 0-486-64927-X .
^ a b c d e de Boer, J. (April 1948). "Quantum theory of condensed permanent gases I the law of corresponding states". Physica . 14 (2–3). Utrecht , Netherlands : Elsevier : 139–148. Bibcode :1948Phy....14..139D . doi :10.1016/0031-8914(48 )90032-9 .
External links [ edit ]
t
e
R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Theorem_of_corresponding_states&oldid=1166026039 "
C a t e g o r i e s :
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● A l l s t u b a r t i c l e s
● T h i s p a g e w a s l a s t e d i t e d o n 1 8 J u l y 2 0 2 3 , a t 2 3 : 0 3 ( U T C ) .
● T e x t i s a v a i l a b l e u n d e r t h e C r e a t i v e C o m m o n s A t t r i b u t i o n - S h a r e A l i k e L i c e n s e 4 . 0 ;
a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n .
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