An accurate evaluation of the speed of sound and heat capacities of refrigeration gases using second virial coefficient with Stockmayer potential

Abstract

In this study, we present an analytical expression to evaluate the speed of sound and heat capacities of refrigerant gases using the second virial coefficient over the Stockmayer potential. The obtained analytical formula yields the accurate and fast evaluation of speed of sound and heat capacities of refrigerant gases. The performance of the suggested approach is verified by its application to the speed of sound and heat capacities calculations of refrigerant gases for R134a, R152a, R718, R32 and R717 in comprehensive range of pressure and temperature. We have also demonstrated that the Stockmayer potential has to be taken into account in the calculations during the evaluation of speed of sound and heat capacities. The obtained results agree well with experimental and theoretical results in the literature.

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Abbreviations

PVT:

Pressure volume temperature

HCFCs:

Hydrochlorofluorocarbons

HFC:

Hydrofluorocarbons

CFC:

Chlorofluorocarbons

EOS:

Equation of state

\( B\left( T \right) \) :

Second virial coefficient (cm3 mol−1)

\( B^{*} \left( {T^{*} } \right) \) :

Reduced second virial coefficient

\( T \) :

Temperature (K)

\( T^{*} \) :

Reduced temperature

C p :

Heat capacity at constant pressure \( ({\text{J}}/{\text{g}}\;{\text{K}}) \)

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

Heat capacity at constant pressure of ideal gases \( ({\text{J}}/{\text{g}}\;{\text{K}}) \)

C v :

Heat capacity at constant volume \( ({\text{J}}/{\text{g}}\;{\text{K}}) \)

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

Heat capacity at constant volume of ideal gases \( ({\text{J}}/{\text{g}}\;{\text{K}}) \)

\( u \) :

Speed of sound (m s−1)

\( \gamma \) :

Heat capacity ratio

\( R \) :

Universal gas constant

\( P \) :

Pressure (Pa)

\( V \) :

Volume (cm3)

\( M \) :

Molecular weight (g/mol)

\( F_{m} \left( n \right) \) :

Binomial coefficient

\( \varGamma \left( \alpha \right) \) :

Gamma function

\( E_{n} \left( z \right) \) :

Exponential integral function

\( \varepsilon \) :

Depth of potential energy minimum (J/mol)

σ :

Value of r at \( u(r) = 0 \) (A0)

k B :

Boltzmann constant (J K−1)

\( \mu \) :

Dipole moment (Debyes)

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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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Correspondence to E. Somuncu.

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Mamedov, B.A., Somuncu, E. & Emek, M. An accurate evaluation of the speed of sound and heat capacities of refrigeration gases using second virial coefficient with Stockmayer potential. Indian J Phys 95, 11–20 (2021). https://doi.org/10.1007/s12648-020-01687-6

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Keywords

  • Refrigeration gases
  • Second virial coefficient
  • Specific heat capacity
  • Stockmayer potential

PACS No.

  • 51.30.+I