Redlich-Kwong equation of state: Difference between revisions
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A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules<ref>[http://dx.doi.org/10.1016/0009-2509(72)80096-4 Giorgio Soave "Equilibrium constants from a modified Redlich-Kwong equation of state", Chemical Engineering Science '''27''' pp. 1197-1203 (1972)]</ref>. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor: | A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules<ref>[http://dx.doi.org/10.1016/0009-2509(72)80096-4 Giorgio Soave "Equilibrium constants from a modified Redlich-Kwong equation of state", Chemical Engineering Science '''27''' pp. 1197-1203 (1972)]</ref>. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor: | ||
:<math>\alpha=\left(1+\left(0.48508+1.55171\omega-0.15613\omega^2\right)\left(1-\sqrt\frac{T}{T_c}\right)\right)^2 </math> | :<math>\alpha(T)=\left(1+\left(0.48508+1.55171\omega-0.15613\omega^2\right)\left(1-\sqrt\frac{T}{T_c}\right)\right)^2 </math> | ||
where <math>T_c</math> is the critical temperature and <math>\omega</math> is the acentric factor for the gas. This leads to an equation of state of the form: | where <math>T_c</math> is the critical temperature and <math>\omega</math> is the acentric factor for the gas. This leads to an equation of state of the form: | ||
:<math> \left[p+\frac{a\alpha}{v(v+b)}\right]\left(v-b\right)=RT</math> | :<math> \left[p+\frac{a\alpha(T)}{v(v+b)}\right]\left(v-b\right)=RT</math> | ||
or equivalently: | or equivalently: | ||
:<math> p=\frac{RT}{v-b}-\frac{a\alpha}{v(v+b)}</math> | :<math> p=\frac{RT}{v-b}-\frac{a\alpha(T)}{v(v+b)}</math> | ||
Revision as of 04:59, 7 November 2011
The Redlich-Kwong equation of state is[1]:
=RT}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ada21aa6800f063a969940dd07f3ecd090c50f65)
where
and
where is the pressure, is the temperature and is the molar gas constant. is the critical temperature and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_c} is the pressure at the critical point.
Soave Modification
A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules[2]. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha(T)=\left(1+\left(0.48508+1.55171\omega-0.15613\omega^2\right)\left(1-\sqrt\frac{T}{T_c}\right)\right)^2 }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_c} is the critical temperature and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega} is the acentric factor for the gas. This leads to an equation of state of the form:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left[p+\frac{a\alpha(T)}{v(v+b)}\right]\left(v-b\right)=RT}
or equivalently:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p=\frac{RT}{v-b}-\frac{a\alpha(T)}{v(v+b)}}
References
- ↑ Otto Redlich and J. N. S. Kwong "On the Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions", Chemical Reviews 44 pp. 233 - 244 (1949)
- ↑ Giorgio Soave "Equilibrium constants from a modified Redlich-Kwong equation of state", Chemical Engineering Science 27 pp. 1197-1203 (1972)