理想气体趋向热平衡态的动力学模拟
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摘要
从动力学出发,导出了二体和三体分子弹性散射的动量分配公式,据此,用计算机模拟了理想气体分子集团长时间碰撞后的行为,证明热平衡态分子动量的麦克斯韦分布主要是由分子的二体碰撞所致,三体碰撞贡献的比例很小.用此方法还研究了器壁对气体动量分布的影响和对气体温度的控制机制,以及气体趋向热平衡的过程.
Based on the momentum distribution theory of two-body and three-body molecular elastic scattering derived from dynamical consideration,a computer simulation was carried out to inspect the behavior of an ideal gas after multiple collisions between molecules,showing that the Maxwell distribution of molecular momentum of the gas in thermal equilibrium state is mainly caused by two-body collision,three-body collision dedicates only a small proportion.Mechanisms of the container's impact to the momentum distribution and to the gas's temperature controlling can be studied with this method,therefore the process of the gas tending to thermal equilibrium state can be traced.
Based on the momentum distribution theory of two-body and three-body molecular elastic scattering derived from dynamical consideration,a computer simulation was carried out to inspect the behavior of an ideal gas after multiple collisions between molecules,showing that the Maxwell distribution of molecular momentum of the gas in thermal equilibrium state is mainly caused by two-body collision,three-body collision dedicates only a small proportion.Mechanisms of the container's impact to the momentum distribution and to the gas's temperature controlling can be studied with this method,therefore the process of the gas tending to thermal equilibrium state can be traced.
引文
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[2]Miller R C,Kusch P.Velocity distributions in Potassium and Thallium atomic beams[J].Phys.Rev.1955,99(4):1314-1321.
[3]曹家骏.分子射线的速率分布的实验[J].大学物理,1987,9:42-45.Cao J J.Experiments on the velocity distribution of molecular[J].College Physics,1987,(9):42-45.
[4]沈慧君,郭奕玲.分子速度分布律的实验验证[J].物理,1989,3:183-187.Shen H J,Guo Y L.Experimental verification of molecular velocity distribution[J].Physics,1989,(3):183-187.
[5]宁长春,曹振鑫,汪亚平,等.奥托·斯特恩实验历史概述[J].大学物理,2015,34(09):39-43.Ning C C,Cao Z X,Wang Y P,et al.An overview of the history of Otto Stern experiment[J].College Physics,2015,34(9):39-43.
[6]Ftacnik J,Lichard P,Pisut J.A simple computer simulation of molecular collisions leading to Maxwell distribution[J].Eur.J.Phys.1983,4(2):68-71.
[7]Bonomo R P,Riggi F.The evolution of the speed distribution for a two-dimensional ideal gas:A computer simulation[J].Am.J.Phys.1984,52(1):54-55.
[8]尤仪.微机模拟导出三维气体分子速率分布[J].福建师范大学学报,1994,10(2):102-106.You Y.An experiment on simulating molecular collisions in three dimensions by microcomputer[J].Journal of Fujian Normal University(Natural Science).1994,10(2):102-106.
[9]李建防,高冰.气体分子的Maxwell速率分布的计算机数据模拟[J].四川工业学院学报,2002,21(2):22-24.Li J F,Gao B.Computer numerical simulation of gaseous molecule Maxwell speed distribution[J].Journal of Sichuan University of Science and Technology.2001,21(2):22-24.
[10]李强,郑彩星,张智.玻尔兹曼分布的计算机模拟[J].大学物理实验,2005,18(4):75-78.Li Q,Zheng C X,Zhang Z.Computer Analogy of Boltzmann distribution[J].Physical Experiment of College,2005,18(4):75-78.
[11]董键.Mathematica与大学物理计算[M].北京:清华大学出版社,2013.