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Virial equation of state for a granular system

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Abstract

The equation of state for an ideal gas is simple, which is \(P=nk_\textrm{B}T\). In the case of imperfect gases where mutual interactions among the constituents are important, pressure P can be expressed as the series expansion of density n with appropriate coefficients, known as virial coefficients \(B_m\). In this paper, we have obtained the first four virial coefficients for a model interaction potential \(\Phi (r)\) using multidimensional Monte-Carlo integration and importance sampling methods. Next, we perform molecular dynamics simulations with the same \(\Phi (r)\) for a many-particle system to obtain P as a function of T and n. We compare our numerical data with the virial equation of state.

Graphic Abstract

The plot of Mayer function f(r) as a function of radial distance r for \(\Theta (r)\) for different inverse temperature \(\beta \).

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All of the data utilized in this manuscript will be made accessible upon reasonable request.

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Acknowledgements

SH acknowledges financial support from IISER Mohali through a Junior Research Fellowship. PD acknowledges financial support from SERB, India through a start-up research grant (SRG/2022/000105).

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Authors and Affiliations

  1. Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, Mohali, Punjab, 140306, India

    Subhanker Howlader & Prasenjit Das

Authors
  1. Subhanker Howlader
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  2. Prasenjit Das
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Contributions

PD proposed the problem and develop the program for molecular dynamics simulation. SH performed the all the analytical and numerical work with the help of PD. The paper was written by PD.

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Correspondence to Prasenjit Das.

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Howlader, S., Das, P. Virial equation of state for a granular system. Eur. Phys. J. E 47, 20 (2024). https://doi.org/10.1140/epje/s10189-024-00412-z

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