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Developing the evaluation method of heat capacity and speed of sound of real gases using fourth virial coefficient over Lennard-Jones (12-6) potential

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Abstract

In this study, we suggest an effective method of the evaluation of HC and SS of real gases by using the FVC over Lennard-Jones (12-6) potential. As known, the determination of the FVC is a key step to correct evaluation of the thermal properties. As an example of application, the suggested method has been performed for gases of Ar, SF6 and SiH4. The obtained results of HC at constant pressure and SS of gases Ar, SF6 and SiH4 are in good agreement with the corresponding theory and experimental data in the range of temperature from 90 to 800 K and range of pressure from 0.09 to 100.7 atm. The precision and accuracy of obtained results from the suggested method have been validated by the literature observations.

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Abbreviations

VDW:

Van der Waals

FVC:

Fourth virial coefficient (cm9 mol−3)

HC:

Heat capacity (kJ/kg K)

SS:

Speed of sound (m s−1)

D(T):

Fourth virial coefficient (cm9 mol−3)

f(r ij):

Mayer function

u(r ij):

Intermolecular interaction

\( C_{\text{P}} \) :

Heat capacities (kJ/kg K)

\( C_{\text{P}}^{0} \) :

Heat capacities of ideal gases (kJ/kg K)

u :

Speed of sound (m s−1)

T :

Temperature (K)

\( k_{\text{B}} \) :

Boltzmann constant (J K−1)

\( N_{\text{A}} \) :

Avogadro number (mol−1)

ɛ :

Depth of potential energy minimum (kcal/mol)

σ :

Value of r at u(r) = 0 (Å)

P :

Pressure (atm)

R :

Universal gas constant (J/mol K)

M :

Molecular weight (g/mol)

γ :

Heat ratio

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Acknowledgements

This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) Science Fellowships and Grant Programmes Department (BIDEB).

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Authors and Affiliations

  1. Department of Physics, Faculty of Arts and Sciences, Giresun University, Giresun, Turkey

    Elif Somuncu

  2. Department of Physics, Faculty of Arts and Sciences, Gaziosmanpaşa University, Tokat, Turkey

    Bahtiyar A. Mamedov

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  1. Elif Somuncu
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  2. Bahtiyar A. Mamedov
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Correspondence to Elif Somuncu.

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Somuncu, E., Mamedov, B.A. Developing the evaluation method of heat capacity and speed of sound of real gases using fourth virial coefficient over Lennard-Jones (12-6) potential. Eur. Phys. J. Plus 135, 454 (2020). https://doi.org/10.1140/epjp/s13360-020-00478-6

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