Dieterici equation of state - Revision history

Carl McBride: /* Sadus modification */ Added an internal link

2010-09-22T14:19:51Z

Sadus modification: Added an internal link

← Older revision		Revision as of 16:19, 22 September 2010
Line 14:		Line 14:
	where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points \| critical]] temperature and <math>P_c</math> is the [[pressure]] at the critical point.		where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points \| critical]] temperature and <math>P_c</math> is the [[pressure]] at the critical point.
	==Sadus modification==		==Sadus modification==
	Sadus <ref>[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]</ref> proposed replacing the repulsive section of the Dieterici equation with the [[Carnahan-Starling equation of state]], resulting in (Eq. 5):		Sadus <ref>[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]</ref> proposed replacing the repulsive section of the Dieterici equation with the [[Carnahan-Starling equation of state]], which is often used to describe the equation of state of the [[hard sphere model]], resulting in (Eq. 5):

	:<math>p = \frac{RT}{v} \frac{(1 + \eta + \eta^2 - \eta^3)}{(1-\eta)^3 } e^{-a/RTv}</math>		:<math>p = \frac{RT}{v} \frac{(1 + \eta + \eta^2 - \eta^3)}{(1-\eta)^3 } e^{-a/RTv}</math>

Carl McBride: /* Sadus modification */

2010-09-22T14:05:36Z

Sadus modification

← Older revision		Revision as of 16:05, 22 September 2010
Line 16:		Line 16:
	Sadus <ref>[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]</ref> proposed replacing the repulsive section of the Dieterici equation with the [[Carnahan-Starling equation of state]], resulting in (Eq. 5):		Sadus <ref>[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]</ref> proposed replacing the repulsive section of the Dieterici equation with the [[Carnahan-Starling equation of state]], resulting in (Eq. 5):

	:<math>p = \frac{RT}{v} \frac{ 1 + \eta + \eta^2 - \eta^3 }{(1-\eta)^3 } e^{-a/RTv}</math>		:<math>p = \frac{RT}{v} \frac{(1 + \eta + \eta^2 - \eta^3)}{(1-\eta)^3 } e^{-a/RTv}</math>

	where <math> \eta = b/4v </math> is the [[packing fraction]].		where <math> \eta = b/4v </math> is the [[packing fraction]].

			This equation gives:

			:<math>a = 2.99679 R T_c v_c</math>

			and

			:<math>\eta_c = 0.357057</math>

	==References==		==References==

Carl McBride: Slight tidy

2010-09-22T14:00:55Z

Slight tidy

← Older revision		Revision as of 16:00, 22 September 2010
Line 1:		Line 1:
	The Dieterici equation of state, ~~proposed in~~ 1899 ~~(Ref. 1~~) is given by		The '''Dieterici''' [[Equations of state \|equation of state]] <ref>C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)</ref> is given by

	:<math>\~~left. p(~~v-b~~) \right.= RT~~ e^{-a/RTv}</math>		:<math>p = \frac{RT}{v-b} e^{-a/RTv}</math>

			where (Eq. 8 in <ref>[http://dx.doi.org/10.1021/ie50663a005 K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry '''57''' pp. 30-37 (1965)]</ref>):

	~~where~~

	:<math>a = \frac{4R^2T_c^2}{P_ce^2}</math>		:<math>a = \frac{4R^2T_c^2}{P_ce^2}</math>
Line 12:		Line 13:

	where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points \| critical]] temperature and <math>P_c</math> is the [[pressure]] at the critical point.		where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points \| critical]] temperature and <math>P_c</math> is the [[pressure]] at the critical point.
			==Sadus modification==
			Sadus <ref>[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]</ref> proposed replacing the repulsive section of the Dieterici equation with the [[Carnahan-Starling equation of state]], resulting in (Eq. 5):

			:<math>p = \frac{RT}{v} \frac{ 1 + \eta + \eta^2 - \eta^3 }{(1-\eta)^3 } e^{-a/RTv}</math>

			where <math> \eta = b/4v </math> is the [[packing fraction]].

	==References==		==References==
	~~# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)~~		<references/>
	~~#[http://dx.doi.org/10.1021/ie50663a005 K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry '''57''' pp. 30 - 37 (1965)]~~
	~~#[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]~~
	[[category: equations of state]]		[[category: equations of state]]

Nice and Tidy at 16:30, 6 February 2008

2008-02-06T16:30:17Z

← Older revision		Revision as of 18:30, 6 February 2008
Line 10:		Line 10:

	:<math>b=\frac{RT_c}{P_ce^2}</math>		:<math>b=\frac{RT_c}{P_ce^2}</math>

			where <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>R</math> is the [[molar gas constant]]. <math>T_c</math> is the [[critical points \| critical]] temperature and <math>P_c</math> is the [[pressure]] at the critical point.
	==References==		==References==
	# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)		# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)

Carl McBride at 10:45, 8 June 2007

2007-06-08T10:45:01Z

← Older revision		Revision as of 12:45, 8 June 2007
Line 1:		Line 1:
	The Dieterici equation of state, proposed in 1899 (Ref. 1) is given by		The Dieterici equation of state, proposed in 1899 (Ref. 1) is given by

	:<math>\left. p(v-b) \right.= kT e^{-a/~~kTv~~}</math>		:<math>\left. p(v-b) \right.= RT e^{-a/RTv}</math>

	where ~~<math>a</math> is an empirical constant.~~		where

			:<math>a = \frac{4R^2T_c^2}{P_ce^2}</math>

			and

			:<math>b=\frac{RT_c}{P_ce^2}</math>
	==References==		==References==
	# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)		# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)
			#[http://dx.doi.org/10.1021/ie50663a005 K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry '''57''' pp. 30 - 37 (1965)]
	#[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]		#[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]
	[[category: equations of state]]		[[category: equations of state]]

Carl McBride at 15:03, 7 June 2007

2007-06-07T15:03:48Z

← Older revision		Revision as of 17:03, 7 June 2007
Line 1:		Line 1:
			The Dieterici equation of state, proposed in 1899 (Ref. 1) is given by

	:<math>\left. p(v-b) \right.= kT e^{-a/kTv}</math>		:<math>\left. p(v-b) \right.= kT e^{-a/kTv}</math>

	where <math>a</math> is an empirical constant.		where <math>a</math> is an empirical constant.

			==References==
			# C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)
			#[http://dx.doi.org/10.1063/1.1380711 Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics '''115''' pp. 1460-1462 (2001)]
	[[category: equations of state]]		[[category: equations of state]]

Carl McBride: New page: : $\left. p(v-b) \right.= kT e^{-a/kTv}$ where $a$ is an empirical constant. category: equations of state

2007-06-07T14:54:10Z

New page: :<math>\left. p(v-b) \right.= kT e^{-a/kTv}</math> where <math>a</math> is an empirical constant. category: equations of state

New page

:<math>\left. p(v-b) \right.= kT e^{-a/kTv}</math>

where <math>a</math> is an empirical constant.
[[category: equations of state]]