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声子气的状态方程和声子气运动的守恒方程
引用本文:过增元,曹炳阳,朱宏晔,张清光.声子气的状态方程和声子气运动的守恒方程[J].物理学报,2007,56(6):3306-3312.
作者姓名:过增元  曹炳阳  朱宏晔  张清光
作者单位:清华大学工程力学系,北京 100084
摘    要:根据爱因斯坦的狭义相对论中质能的等效关系,把固体(本文指非导体)晶格(原子)的质量分为晶格(原子)的静质量和晶格热振动能量的等效质量两个部分,后者就是固体中声子气的等效质量.晶格(原子)热振动的能量则分为晶格(原子)静质量具有的热能以及声子气质量具有的热能.基于固体的状态方程,导得了晶格静质量热振动的状态方程和声子气的状态方程.声子气在固体介质中的宏观运动就是热量在固体中的传递过程.建立了声子气运动的守恒方程组,分析表明,忽略惯性力时声子气的动量守恒方程就退化为傅里叶导热定律,阐明了傅里叶导热定律的物理本质是声子气驱动力与阻力的平衡方程.当热流密度很大惯性力不能忽略时,傅里叶导热定律不再适用. 关键词: 非傅里叶导热 声子气 声子气质量 状态方程 守恒方程

关 键 词:非傅里叶导热  声子气  声子气质量  状态方程  守恒方程
文章编号:1000-3290/2007/56(06)/3306-07
收稿时间:8/1/2006 12:00:00 AM
修稿时间:2006-08-01

State equation of phonon gas and conservation equations for phonon gas motion
Guo Zeng-Yuan,Cao Bing-Yang,Zhu Hong-Ye,Zhang Qing-Guang.State equation of phonon gas and conservation equations for phonon gas motion[J].Acta Physica Sinica,2007,56(6):3306-3312.
Authors:Guo Zeng-Yuan  Cao Bing-Yang  Zhu Hong-Ye  Zhang Qing-Guang
Institution:Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Abstract:Based on the mass-energy relation of Einstein's relativity theory, the mass of solid lattices is divided into two parts: the rest mass of solid atoms and the equivalent mass of thermal vibration energy of lattices. The latter is exactly the equivalent mass of the phonon gas in a solid. The vibration energy of the solid lattices includes the thermal energies consisting of the rest mass of the solid lattices and the equivalent mass of the phonon gas. The state equations for the lattice rest mass and the phonon gas are deduced based on the state equation of solids. The heat conduction is just the motion of the phonon gas in a solid. The conservation equations for the phonon gas motion are established. It is found that the conservation equation of phonon gas momentum degenerates to the Fourier's conduction law when the inertial force of the phonon gas can be ignored. The physical nature of the Fourier's law is the balance between the driving force and the resistance for the motion of the phonon gas. Under ultrahigh heat flux conditions where the inertial force is too high to be ignored, the Fourier's law is no longer valid even under the steady condition.
Keywords:non-Fourier heat conduction  phonon gas  mass of phonon gas  state equation  conservation equation
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