摘要:
在热力学中,一个封闭体系的完全物态方程指由两个状态量为自变量所确定的一种函数关系,由这个关系能够导出所有其他热力学量之间的关系。比如亥姆霍兹自由能F表示为体系的比体积v和温度T的函数F (v, T )时,就是这种完全物态方程。但是这种完全物态方程至今没有实际计算的表达式。我们以等温压强函数pT (v)和建立在德拜模型基础上的定容比热函数Cv(v, T )为基础,建立了一个有具体函数表达式的完全物态方程。用这种完全物态方程对几种固体金属材料进行了实际计算,所导出的热力学状态量和物性参数,与实验测量能够比较好地符合。这种完全物态方程在高温高压物理领域具有一定的应用价值。
Abstract:
In thermodynamics, the complete equation of state (EOS) for closed system is a functional relation defined by two independent state variables, and all other thermodynamic relations can be deduced by it. For example, Helmholtz free energy F as a function of specific volume v and temperature T of the system is a complete EOS. Unfortunately, the concrete expressions of these complete EOSs are unavailable. Here we establish a practical form of the complete EOS based on the pressure function pT (v) and constant-volume specific heat function Cv(v, T ) This complete EOS is mathematically equivalent to the Helmholtz free energy F . Here pT (v) is determined by the measurement and Cv(v, T ) can be expressed by two parts. One part is the lattice contribution based on the Debye model and the other part is electronic contribution obtained from the free electron model. Using this complete EOS we calculate the isothermal equation for six metals from the Hugoniot data. Good agreement between the isothermal equation and the experimental data verifies the reliability of the complete EOS. Through this complete EOS we can derive the concrete expression of physical parameters, and these physical parameters including the volume expansion coe?cient, the volume speed of sound, the adiabatic modulus, and W-J coe?cient are calculated by using the experimental data of Cu. Analyzing their variation trends we can timely adjust parameter in the calculation of the EOS. This kind of complete EOS is useful in the field of high temperature and high pressure physics.
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