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摘要: 对体积物态方程v-vc=(R/p)(h-hc)的物理基础进行了讨论。给出了该方程的一个统计力学形式证明,从而给出了方程中物质参数的微观定义,亦即给出了该方程的具体表达式。在R=R(p)假设下,给出了方程中物质参数的热力学表达式,通过分析其与Debye理论下的对应态定律的一致性,证明了该假设的近似合理性,从而也就证明了该方程的成立并不受其建立时所依据的定压比热为常数这一过强条件的限制。进一步地,通过与物质参数热力学表达式常压实验值的比较,指出了单纯的R=R(p)假定存在一定的局限,该局限引起的偏差随温度的升高而增大,在常压下的高温区间,该偏差在20%左右。Abstract: A new equation of state v-vc=(R/p)(h-hc) with the assumption R=R(p) (where v, p, h are specific volume, pressure and specific enthalpy respectively, R is substance parameter, the subscript c refers to the state not depending temperature), has been used in the study of the shock compression of porous materials, since it was developed by Qiang Wu et al. However, this EOS was on the basis of the assumption that the specific heat at constant pressure cp remains constant, so its physics base about the EOS has not been proved and the concert form was not got. In this paper, a proof to the N-EOS was finished with solid physics and statistical mechanics, and the normal formula of substance parameters was obtained in microphysics. We also proved that the physics base of the N-EOS with R=R(p) is in correspondence with the law of states of the Debye theory and its validity is not limited by the assumption which the cp remains constant. In addition, the calculation results of R with experimental data under normal pressure shows that R=R(p) is not very accurate approximation. A tentative discussion about the problem of =(v) approximation of the Gruneisen EOS was done.
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Key words:
- equation of state /
- statistical mechanic /
- solid state physics
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经福谦. 实验物态方程导引 [M]. 北京: 科学出版社, 1986. 徐锡申, 张万箱. 实用物态方程理论导引 [M]. 北京: 科学出版社, 1986. Wu Qiang, Jing Fuqian. A New Thermodynamic Equation of State [J]. J Appl Phys, 1995, 80(8): 4343-4349. 朗道Л Д, 栗弗席兹E M. 统计物理学 [M]. 杨训恺译. 北京: 人民教育出版社, 1964. 钱学森. 物理力学讲义 [M]. 北京: 科学出版社, 1962.
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