Equation of state for gaseous nitrogen determined from isotropic model potentials

Abstract

A four-term virial equation of state was combined with isotropic potential models to predict accurate volumetric and caloric thermodynamic properties of nitrogen in the gas phase. The parameters of the model potentials were determined from a fit to acoustic data alone; no other data was used. For nitrogen, it was only necessary to approximate the fourth virial coefficient at the level of interactions that contained no more than one triplet potential; higher order approximations offered no further advantage. It was shown that the four-term virial equation was more accurate than the three-term analogue. It was found that predicted virial coefficients became consistent with experimental values when temperature was >150 ± 30 K; conversely, below this range virial coefficients predicted by the model did not agree with experiment. It was believed that predicted fourth virial coefficient was reliable and accurate only above about 150 K. Predicted compressibility factors deviated by <0.05% at pressures of up to 10-12 MPa, or densities up to 4 mol/dm 3 (≈0.4 c ), only when temperature was >220 K. Values of enthalpy predicted from the equation of state showed good agreement with experimental data.Uneéquation d'état virialeà quatre termes aété combinée avec des modèles de potentiel isotropique afin de prédire avec précision les propriétés volumétriques et caloriques thermodynamiques de l'azote en phase gazeuse. Les paramètres des potentiels de modèle ontété déterminésà partir d'une adaptation unique aux données acoustiques. Aucune autre donnée n'aété utilisée. Pour l'azote, il est seulement nécessaire d'approximer le quatrième coefficient virial au niveau des interactions qui ne contiennent pas plus d'un potentiel de triplet; les approximations d'ordre supérieur n'offrent pas d'avantages supplémentaires. On a montré que l'équation virialeà quatre termes est plus précise que l'analogueà trois termes. Il aété conclu que les coefficients viriaux prédits correspondaientà 30 K. Réciproquement, les valeurs expérimentales correspondantà une température de plus de 150 en-dessous des coefficients viriaux de cet intervalle prédits par le modèles ne sont pas en accord avec l expérimentation. Je considère que le quatrième coefficient virial prédit n'est fiable et précis qu'au-dessus d'environ 150 K. Les facteurs de compressibilité prédits dévient de moins de 0,05 pour centà des pressions pouvant atteindre jusqu'à 10-12 MPa ou des densités pouvant atteindre jusqu'à 4 c), seulement lorsque la température est supérieureà 220 K. Les valeurs de 0,4 ≈ mol/dm3 (l enthalpie préditeà partir de l équation d'état montraient une bonne correspondance avec les données expérimentales.

Virial coefficients of nitrogen from a quadrupolar site–site potential function

“…Values of the perfect-gas heat capacity required to calculate acoustic virial coe±cients were determined as in Ref. 10. Figure 1 compares values of B calculated in this way with the experimental data of several authors.…”

“…(17) the three-body strength coe±cient for nitrogen was required; for this, we used the value # 123 /k ¼ 0:001 K nm 9 which was suggested by results from previous work. 10 The application of Eq. (8) requires knowledge of the quadrupole moment for nitrogen; for this, the value  ffiffiffi k p ¼ À0:396 (K nm 5 Þ 1=2 reported by Hurt and Bose 24 was used.…”

“…However, at low reduced temperatures second and third virial coe±cients of nonspherical molecules determined in this manner have exhibited clear signs of systematic deviations from experimental values. 5,6,[8][9][10] These deviations are probably due, in part, to errors in the experimental virial coe±cients, but also due to inaccuracies in the models which only become apparent at low temperatures. In the case of the second virial coe±cient of nitrogen, it was shown that agreement between calculated and experimental values improved markedly when the isotropic potential in the model was replaced with an anisotropic pair potential function.…”

Comment on “An equation of state for gaseous argon determined from the speed of sound”

“…We strongly discourage from its use, particularly as correct parametrizations for fourth- [14] and higher-order [18] virial EOS for Argon have been reported recently. We also discourage from employing ad hoc ''approximations'' [7,[10][11][12][13] to the 3-body or, generally, the non-additive contributions to D, and have shown that such ''approximations'' may, in fact, overestimate these contributions significantly. We consequently disagree with Ref.…”

“…[1] -similarly to elsewhere [10][11][12] and to Trusler [13] -cites diagrammatic works of Casanova et al [6] and Dulla et al [7], neither justify to discard products of f ijk 's in any other than an ad hoc fashion.…”