Thermodynamic Properties And Nonlinearity Acoustic Parameters Of Liquid Sodium At High Pressure Calculated By Equation Of State

Acquiring reliable thermodynamic properties in liquid metals at high pressure and temperature is still a challenge in both experiment and theory.The equation of state provides researchers with a solution to these challenges.The equation of state of the material can be used to describe the material state,that is,the relationship between the various thermodynamic parameters of the material,such as,pressure,temperature,volume,internal energy and the heat capacity.A good Eo S can often provide qualitative information of thermodynamic properties of a system through a limited number of measurements at various temperature and pressure.However,so far,no equation of state can be satisfactorily applied to all engineering analysis,so the study of the equation of state is still very active.Our purpose here is to examine if certain simple forms of EoS,such as the power law form,for liquids are suitable for calculation of thermodynamic properties that have not been obvious and easy to obtain so far.In this paper,we provide a function of the thermodynamic properties of liquid sodium under the isotherm by using the state equation of power form,including,the isothermal bulk modulus,thermal expansion coefficient,heat capacity,internal pressure,heat capacity,Gruneisen parameter and Anderson-Gruneisen parameter.Then,the expressions for acoustical parameter and nonlinearity parameter are obtained based on thermodynamic relations from an equation of state with a power lawform.Both parameters for liquid Sodium are calculated under high pressure along the isothermal lines by using the available thermodynamic data and numeric derivations.The relation between the isochoric acoustical parameter and internal pressure is derived and the corresponding approximation at low pressure condition is discussed.By simulation,the results are in excellent agreement with available experimental data measured by a piezometer at high temperature and high pressure and sound velocity measurement with pulse-echo technique.We found that the pressure derivative of the isothermal bulk modulus at zero pressure is a monotonic function of temperature and has a value around 4.In addition,unexpected crossing points were found in the isobaric thermal expansion coefficient and Gruneisen parameter;and a minimum in the isobaric heat under isothermal compression was also observed.A minimum of isobaric heat capacity along the isothermal paths is predicted with the minimum positions shifting to the higher pressure with increasing temperature.Both the calculated adiabatic bulk modulus and the sound velocity increase with pressure along the isothermal paths.The obtained heat capacity ratio is found to increase with pressure along the isothermal paths and a crossing point is observed.For nonlinear parameters,(7)B/A(8)'was found to be positive and increasing with pressure although(7)B/A(8)'was negative and its magnitude was small and increasing with the pressure.there is no simple linear function to describe the relation between(7)B/A(8)and(7)1/C_S(8)in liquid sodium from calculation and other organic liquids from experimental data.As an empirical behavior,Ballou's rule may be used to roughly estimate the mean nonlinearity parameter in liquids but cannot provide any quantitative information about(7)B/A(8)for some specific liquid over certain pressure range.And a universal relation between(7)B/A(8)and(7)1/C_S(8)for all liquids still remains unattained,although several theoretical models have been developed.While some of these detailed predictions are yet to be confirmed by further experiment,our results suggest that the power law form may be a more suitable choice for the EoS of liquids metals.