Influence of potential attraction term on Joule-Thomson coefficient, enthalpy and entropy of real gases

https://doi.org/10.1016/j.physb.2021.413418Get rights and content

Highlights

  • Two different intermolecular potentials are considered for the three real gases.

  • The effect of attraction term of the potential models on thermophysical function is studied.

  • We can select the suitable potential model to give better results in comparison with experimental data.

Abstract

In the present work, two different intermolecular potentials are considered for the three real gases such as Ar, Kr and Xe. The effect of attraction term of the potential models on internal energy, enthalpy, entropy and Joule-Thomson (JT) coefficient of aforementioned gases has been investigated. To This end, the second virial coefficient of each potential was analytically derived. The suggested potential models have different attraction terms and the same repulsive terms. Our theoretical results in this work have been compared with experimental data. Our results reveal that the attraction term of the interaction potential has an important and main role to the thermodynamic properties of the selected gases. According to the results, it is found that the calculated thermodynamic function of the aforementioned gases obtained using both potential models are in acceptable agreement with available data. The degree of agreement depends strongly on the type of the used potential model and the range of pressures and temperatures. For instance, the JT coefficient of the Kr gas calculated by potential model (1) at high pressures and temperatures are in good agreement with experimental results. This property for the Ar gas has better agreement when we employ the potential model (2). This work allows us to select the suitable potential model and desired rages of pressure and temperature to give better results in comparison with experimental data.

Introduction

The knowledge of thermal and transport properties of real gases plays an important role in engineering and industrial applications [[1], [2], [3], [4], [5], [6]]. The prediction of thermal properties of real gases in a wide range of temperature and pressure is one of the exciting problems in condensed matter physics, physical chemistry, chemistry and chemical engineering [[7], [8], [9], [10]].

Among the thermodynamic properties of gases, the enthalpy, entropy and Joule-Thomson (JT) coefficient are important properties. The cooling produced in the JT expansion makes it a valuable tool in refrigeration [11,12]. Therefore, the information about JT coefficient can be used to design of industrial refrigerators. Also, enthalpy is used to evaluate the heat of reaction of a chemical process. Change in enthalpy is employed to measure heat flow in calorimetry. In addition, measuring the change in enthalpy can be used to determine whether a reaction is endothermic or exothermic. Entropy can be considered as a measure of the quality of heat energy in relation of temperature [13].

There are some theoretical and experimental methods to evaluate the thermodynamic functions of gases. Examples of experimental methods are pressure vessel, radiation shield, Inlet tube and Cryostat [14,15]. The virial equation of state (EOS) is an important and interesting method to predict thermodynamic functions of gases. In the virial EOS, one should obtain the virial coefficients as a function of temperature. In the most papers, authors have employed the virial EOS until the second coefficient [[16], [17], [18], [19], [20]]. The enthalpy, entropy and Joule-Thomson (JT) coefficient in a gas can be theoretically determined by using the Gibbs free energy [[21], [22], [23]].

It is worthy mentioned that the knowledge of intermolecular interaction (interaction potential) in a given system like a real gas is necessary for evaluating the virial coefficients and thereby thermodynamic functions [24,25]. Hitherto, several interaction potentials have been applied to compute the virial coefficients, in particular, the second virial coefficient [[26], [27], [28], [29], [30], [31], [32]]. We can say that one of the most famous interaction potential is the Lennard-Jones (LJ) potential. It is used for studying the thermodynamic and transport properties of the noble gases in many papers in the past two decades. Recently, using the improved Tietz potential model and its special cases to represent the internal vibrations of diatomic molecules or triatomic molecules, some authors successfully predicted the thermodynamic properties for some pure substances, including the H2, HCl, CO, NO, N2, H2O, H2S, and CO2 [[33], [34], [35], [36], [37], [38], [39], [40], [41]].

Noble gases such as argon (Ar), krypton (Kr) and xenon (Xe) are colorless, dens, odorless and with very low reactivity. The gases have important potential applications in the various branches of sciences. For example, the xenon gas is used in light-emitting devices and in photographic flashes and stroboscopic lamps and it is present at about 90 ppb in earth's atmosphere. Argon is used in graphite electric furnaces to prevent the graphite from burning. Argon can be used as the carrier gas in gas chromatography and in electrospray ionization mass spectrometry. Krypton is used occasionally as an insulating gas between window panes. Krypton is mixed with argon in energy efficient fluorescent lamps, reducing the power consumption. Therefore, accurate knowledge of the thermodynamic and transport of the gases is one main challenge in engineering.

Here, we consider two interaction potential models which their attraction terms are different from the LJ potential model. Using the potential models, we determine the entropy, enthalpy, JT coefficient and internal energy of noble gases like Ar, Kr and Xe. Then, we compare our theoretical results with the experimental available data. After comparing, we can found the role of the attraction term of the potential model in obtaining the aforementioned properties.

Section snippets

Potential models

It is fully known that knowledge of interaction potential of a given system has an important role in obtaining its physical properties. In this part, we introduce two interactions potential models. The potential models are as [42].

  • i)

    Potential model (1)u(r)=ε{(σr)12sech2[λ(rσ)λ]},

  • ii)

    Potential model (2)u(r)=ε{(σr)12exp([μ(rσ)μ]2)},

Here, ε and σ are the energy scale and the length scale, respectively. In above equation, we have selected λ=2.3 and μ=2.0. The parameters λ and μ are selected so that

Results and discussion

In this part, we present our theoretical results for the entropy, internal energy, enthalpy and JT coefficient of three different gases like Ar, Kr and Xe. For this purpose, we have calculated the aforementioned properties using two different potential models and compared with the experimental data [44].

In Fig. 1, we have shown the variations of two potential models versus the molecular distance. In this figure, the (12–6) Lannard-Jones potential is also plotted.

To display the accuracy our

Conclusion

In the present paper, three real gases such as Ar, Kr and Xe have been considered. We have selected the gases due to potential applications in various branches of science. We have introduced two interaction potentials with different attraction terms but the same repulsion terms. For this purpose, we have used the (12–6) Lennard-Jones potential and changed the attraction term of the potential. Then, the internal energy, enthalpy, entropy and JT coefficient of aforementioned gases have been

Author contribution

Ahmad Ghanbari and Reza Khordad conceived of the presented idea. Ahmad developed the theory and performed the computations. Reza verified the analytical methods and investigate the findings of this work. All authors discussed the results and contributed to the final manuscript. The descriptions are accurate and agreed by all authors.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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