A Transformation Formula for Determining the Second Density Virial Coefficient from the Second Acoustic Virial Coefficient

The Euler–Cauchy-type differential equation relating the second density virial coefficient B and the second acoustic virial coefficient β a is solved in order to obtain an analytical transformation formula for determining the temperature dependence of B from that of β a , under an assumption that th...

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Bibliographic Details
Published in:International journal of thermophysics 2022-05, Vol.43 (5), Article 64
Main Author: Tada, Kohei
Format: Article
Language:English
Subjects:
Classical Mechanics
Condensed Matter Physics
Density
Differential equations
Geophysics
Ideal gas
Industrial Chemistry/Chemical Engineering
Methane
Physical Chemistry
Physics
Physics and Astronomy
Temperature dependence
Thermodynamics
Virial coefficients
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Summary:The Euler–Cauchy-type differential equation relating the second density virial coefficient B and the second acoustic virial coefficient β a is solved in order to obtain an analytical transformation formula for determining the temperature dependence of B from that of β a , under an assumption that the ideal-gas specific heat ratio γ 0 is constant. The obtained formula is verified using the thermophysical data of helium-4, nitrogen and methane gases. For species that are not monatomic γ 0 depends on temperature, and the magnitude of the errors introduced by this assumption is estimated in the case of nitrogen and methane.
ISSN:0195-928X
1572-9567
DOI:10.1007/s10765-022-02992-4