Van der Waals equation of state: Difference between revisions

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* <math> R  </math> is the Gas constant; <math> R = N_A k_B </math>, with <math> N_A </math> being [[Avogadro constant]]
* <math> R  </math> is the Gas constant; <math> R = N_A k_B </math>, with <math> N_A </math> being [[Avogadro constant]]


The VDW equation of state (EoS) takes into account two features that are absent in the Ideal Gas (EoS):
The Van der Waals equation of state takes into account two features that are absent in the [[Equation of State: Ideal Gas | ideal Gas]] equation of state:


The parameter <math> b </math> introduces somehow the '''repulsive behavior between pairs of molecules at short distances''',  
The parameter <math> b </math> introduces somehow the '''repulsive behavior between pairs of molecules at short distances''',  
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whereas <math> a </math> measures the '''attractive interactions''' between the molecules
whereas <math> a </math> measures the '''attractive interactions''' between the molecules


The VDW EoS leads to a liquid-vapor equilibrium at low temperatures, with the corresponding critical point
The Van der Waals equation of state leads to a liquid-vapor equilibrium at low temperatures, with the corresponding critical point

Revision as of 15:38, 23 February 2007

The van der Waals (VDW) equation is

.

where:

  • is the pressure
  • is the volume
  • 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 n } is the number of moles
  • 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 } is the absolute temperature
  • 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 R } is the Gas constant; 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 R = N_A k_B } , with 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 N_A } being Avogadro constant

The Van der Waals equation of state takes into account two features that are absent in the ideal Gas equation of state:

The parameter Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle b} introduces somehow the repulsive behavior between pairs of molecules at short distances, it represents the minimum molar volume of the system.

whereas 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 a } measures the attractive interactions between the molecules

The Van der Waals equation of state leads to a liquid-vapor equilibrium at low temperatures, with the corresponding critical point

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