Study On The Nonextensivity Of A Real Gas

Nonextensive statistics is a new statistical theory based on q-entropy which was proposed by Tsallis in 1988.It is a generalization of the classical Boltzmann-Gibbs statistical theory,which can solve some problems in complex system including long-range interaction systems and so on.The investigation of nonextensive statistics and its applications is in the international hot fields in the research of physical foundation.In this paper,we discuss the basic theory of nonextensive statistical mechanics and its applications in some fields such as astrophysics,plasma physics and chemical physics etc.Our work focus on the nonextensivity of a real gas,including the relationships between the nonextensive q-parameter and the two modification coefficients a and b in the van der Waals’equation,and the Joule-Thomson coefficient of the gas throttling expansion process in nonextensive statistics.We introduce three thermodynamic relations based on physical temperature and physical pressure in nonextensive thermodynamics.They are the Joule-Thomson coefficient,the thermodynamic relation between the constant volume heat capacity and the constant pressure heat capacity,and the ratio of the adiabatic compression coefficient and the isothermal compression coefficient.As compared these thermodynamic relations with the classical forms,we show that the traditional thermodynamic relationships are not extended in parallel to the corresponding forms in nonextensive thermodynamics,and the Joule-Thomson coefficient can be used to study the throttle expansion process in a complex gas obeying the power-law q-distributions.We study the two correction coefficient a and b in the van der Waals’equation in nonextensive statistics.The two coefficients can be expressed by the nonextensive parameter q and the state parameters of a real gas,such as volume,temperature,pressure,and molecular number of the gas,and so the two correction coefficients a and b in nonextensive statistics are not constant as they are given in traditional statistics.We also derive two new expressions of the nonextension parameter q for the real gas,which not only contain the state parameters of the real gas,but also contain the interaction Lenard-Jones potential between molecules and the molecular number.We therefore get the conclusions that a real gas is basically extensive,and only when the gas is a small system containing a limited number of molecules or it is the so-called few body system,the nonextensivity plays a significent role in the real gas and its van der Waals’equation.The conclusions have obtained the experimental test of the real gases by using the experimental data of the five real gases:CO₂,N₂,O₂,H₂and He.