Chapter 16 Kinetic Theory of Gases 理想气体的微观模型 1)分子可视为质点;线度d~10-m, 间距r~10m,d<r 2)除碰撞瞬间,分子间无相互作用力; 3)弹性质点(碰撞均为完全弹性碰撞); 4)分子的运动遵从经典力学的规律
Chapter 16 Kinetic Theory of Gases 1）分子可视为质点； 线度 间距 ; ~10 m, −10 d r d r − ~10 m, 9 2）除碰撞瞬间, 分子间无相互作用力； 理想气体的微观模型 4）分子的运动遵从经典力学的规律 . 3）弹性质点（碰撞均为完全弹性碰撞）；
Chapter 16 Kinetic Theory of Gases Chapter 16 Kinetic Theory of Gases (气体动理论) 1. Molecular interpretation of Temperature 2. Distribution of Molecular Speed 3. Mean Free Path
Chapter 16 Kinetic Theory of Gases Chapter 16 Kinetic Theory of Gases （气体动理论） 1. Molecular interpretation of Temperature 2. Distribution of Molecular Speed 3. Mean Free Path
Chapter 16 Kinetic Theory of Gases Root mean square:方均根速率 Maxwell distribution of speeds 麦克斯韦速率分布率 Mean free path平均自由程
Chapter 16 Kinetic Theory of Gases Root mean square: 方均根速率 Maxwell distribution of speeds 麦克斯韦速率分布率 Mean free path 平均自由程
Chapter 16 Kinetic Theory of Gases 8 16-1 Molecular Interpretation of Temperature (384-388) This section is typical method of m IcroscopIc research which is called kinetic theory of gases. Kinetic theory is based on an atomic model of matter. The basic assumption of kinetic theory is that the measurable properties of gases combined actions of countless numbers of atoms and molecules
Chapter 16 Kinetic Theory of Gases §16-1 Molecular Interpretation of Temperature (384-388) This section is typical method of microscopic research which is called kinetic theory of gases. Kinetic theory is based on an atomic model of matter. The basic assumption of kinetic theory is that the measurable properties of gases combined actions of countless numbers of atoms and molecules
Chapter 16 Kinetic Theory of Gases 1 Velocities based on statistics Statistical Hypotheses(统计假设 (a) Velocities of molecules are different. Each molecule has its velocity, which may be changed due to collisions (b) At equilibrium, the distribution of molecules on the position is uniform, which means that the density of number of molecules is the same everywhere
Chapter 16 Kinetic Theory of Gases 1 Velocities based on statistics: Statistical Hypotheses(统计假设): (a) Velocities of molecules are different. Each molecule has its velocity, which may be changed due to collisions; (b) At equilibrium, the distribution of molecules on the position is uniform, which means that the density of number of molecules is the same everywhere
Chapter 16 Kinetic Theory of Gases 分子按位置的分布是均匀的dNN (C)At equilibrium, velocity of each molecule has the same probability to point to any directions. That is, the distribution of velocity of molecules is uniform in direction. which leads to the mean square speeds of all components of velocity are same 分子各方向运动概率均等,即分子按方向的分布 是均匀的
Chapter 16 Kinetic Theory of Gases V N V N n = = d d 分子按位置的分布是均匀的 (C) At equilibrium, velocity of each molecule has the same probability to point to any directions. That is, the distribution of velocity of molecules is uniform in direction, which leads to the meansquare speeds of all components of velocity are same. 分子各方向运动概率均等，即分子按方向的分布 是均匀的
Chapter 16 Kinetic Theory of Gases 4分子运动速度可=01+0b7+k 2分子平均速度 由于分子沿x轴正向和x轴负向的运动概率是相 同的,因此,在x方向上分子的平均速度为0。 71x+2x+…+=0 同样有,=0,2=0 7=7=0
Chapter 16 Kinetic Theory of Gases vx = vy = vz = 0 i j k i ix iy iz v = v + v + v 由于分子沿 x 轴正向和 x 轴负向的运动概率是相 同的，因此，在 x 方向上分子的平均速度为 0 。 分子运动速度 分子平均速度 0 1 2 = + + + = N x x Nx x v v v v 同样有 = 0, vy vz = 0
Chapter 16 Kinetic Theory of Gases 分子速度在x方向的方均值: mean-square speeds U:三 201+⑦2,+…+0Nx 2 ∑ 同理,分子速度在y、2方向的方均值: N
Chapter 16 Kinetic Theory of Gases = i x ix N 2 1 2 v v 分子速度在x方向的方均值： 同理，分子速度在y、z方向的方均值： mean-square speeds N x 2 Nx 2 v + v2 x + + v = 1 2 = i x ix N 2 1 2 v v , 2 1 2 = i y iy N v v = i z iz N 2 1 2 v v
Chapter 16 Kinetic Theory of Gases There is no preference to one direction or another2 由矢量合成( combine)法则,分子速度的方均值为 2 0=0+0+0 2=30 各方向运动概率均等 y ∑
Chapter 16 Kinetic Theory of Gases 2 2 2 2 3 1 各方向运动概率均等 vx = vy = vz = v There is no preference to one direction or another 由矢量合成(combine)法则，分子速度的方均值为： 2 2 2 vx = vy = vz 2 2 2 2 2 v = vx + vy + vz = 3vx = = i x i x N 2 2 1 2 3 1 v v v
Chapter 16 Kinetic Theory of Gases 2 Pressure Formula of ideal gases 设边长分别为x、y及z的长方体中有N个全同的 质量为m的气体分子,计算A1壁面所受压强 y 10 1770 2
Chapter 16 Kinetic Theory of Gases 2 Pressure Formula of Ideal Gases: mvx mvx - A2 v o y z x y z x A1 v y v x v z v o 设 边长分别为 x、y 及 z 的长方体中有 N 个全同的 质量为 m 的气体分子，计算 壁面所受压强 . A1