《E气体动理论》PPT课件.ppt

Introduction In our study of dynamics, we developed methods to calculate energy. An object have kinetic energy, gravitational potential energy, or elastic potential energy. To calculate the total energy of a collection of objects, we would simply add up the contributions made by each object. However, many physical system contain an impossibly large number of separate object. For instance, a jug of water contains an enormous number of water molecules, and we can hardly calculate the energy of the water by adding up the contributions from each molecule. What can we say about the energy of such a system and energy exchanges that occur when it interacts with other systems?,In following chapters, we consider these questions. In chapter 18, first, we seek to do so using only macroscopic physical properties; by this we mean measurable properties of bulk system that take no heed of its microscopic constituents. Then, we want to find the relationship between macroscopic and microscopic physical quantities. In chapter 19, we shall concentrate on the first and second laws of thermodynamics. The first law of thermo-dynamics expresses the relationship more formally by explicitly introducing a heat flow term into the energy conservation. This clarification of energy conservation, which was one of the great triumphs of nineteenth-century physics, arose almost by consensus from the work and thoughts of many leading scientists of the time.,气体动理论和热力学基础 The foundations of Gas kinetics and thermodynamics,1 研究对象,物质的热运动和热运动与其它形式的运动之间相互转化所遵循的规律,热现象及其规律,组成宏观物体的大量微观粒子(分子、原子)的一种永不停息的无规则的运动。,热运动：,热现象：,组成宏观物体的大量微观粒子热运动的集体表现,凡是与温度有关的物理现象都是热现象.,热运动是热现象的微观实质 热现象是热运动的宏观表现,实例: 物体受热温度升高,体积膨胀,冰受热融化为水等,2 研究方法,以物质的分子、原子结构概念和分子热运动概念为基础, 将微观运动和宏观运动相联系,应用统计的方法,解释并揭示物质宏观热现象及其有关规律的本质,确立宏观量和微观量之间的关系系。 (1) 热运动 (2) 微观量，宏观量 (3) 统计规律,Gas kinetics 气体动理论：,(1) 就整体而言, 在一定状态下,物质具有一定的能量; (2) 从一个状态过度到另一个状态,遵从一定规律,Thermodynamics 热力学：,不涉及物质的微观结构，根据由观察和实验总结得出的热力学定律，从能量观点出发，分析研究在物质状态变化过程中有关热功转化的关系和条件,Chapter 18 Gas kinetics,1 Equilibrium state Equation of state 2 Pressure formula for ideal gas 3 Temperature and Energy 4 Theorem of equipartition of energy The internal energy of idea gas 5 Maxwell speed distribution law 6 Molecular mean collision frequency Mean free path 7 Transport phenomena in gas 8 Application,1 Equilibrium state Equation of state,1 Equilibrium state 平衡状态,Notes, Without external action (influence): Neither doing work nor heat transfer, Macroscopic characteristics do not change with time,The state that macroscopic characteristics do not change with time without external action (influence), thermodynamical equilibrium 热动平衡,无外界影响时宏观性质不随时间变化的状态,(1) Equilibrium state 平衡状态,(2) State parameters 状态参量 V P T,Volume 体积V,Temperature 温度T,Pressure 压强P,2 Equation of state of ideal gas 理想气体状态方程,Boyles law: For a given sample of gas at a fixed temperature, the product of the pressure P and the volume V is constant: PV =constant Gay-Lussacs law: The volume of a given amount of any gas is proportional to the absolute temperature when the pressure is held constant ： V/T=constant Charless law: The pressure is proportional to the absolute temperature when the volume is held constant ： P/T=constant,Equilibrium state 平衡状态,F(V P T)=0,Any object in thermaldynamicaal equilibrium are at the same temperature Thermodynamic scale: Kelvin scale T =273.15 +t The zeroth law of thermodynamics: If objects A and B are each in thermal equilibrium with an object C, then they are also in thermal equilibrium with each other.,Molar gas constant,=constant,Appendix:,Example: Calculate the density of oxygen at STP (standard temperature and pressure). The molecular mass of oxygen is 32g, and it closely obeys the ideal gas equation of state under this condition.,Solution: Consider a quantity of 1 mol of oxygen that has a mass of 32g and contains 6.0221023 molecules.,To calculate the density:,The molecular model of ideal gas -microscopic definition 理想气体的分子模型-微观定义,2 Pressure formula for ideal gas,The self size of molecules is far smaller than the average distance between molecules, being neglect 分子本身的线度远小于分子平均间距,可忽略不计,(2) The interactions between molecules and the wall of container are neglected except the instant of collisions 除碰撞瞬间，忽略分子之间、分子与器壁之间的相互作用。,(3) The collisions between molecules and the wall of container are perfect elastic collisions 分子之间、分子与器壁之间的碰撞是完全弹性,2 The dominant idea 主导思想,(1) Idea: 观点,Macroscopically 宏观 Force per unit area,Microscopically 微观 The constant, rapid drumbeat of molecules bouncing off the wall of the container exerts a steady average force on the wall,(2) Method 方法:,(3) Result 结果:,The average kinetic energy of a single molecule 一个分子的平均平动动能,n: Number density of molecules 分子数密度,Statistical method 统计方法,3 The derivation of pressure formula压强公式的推导,M,m,Gas is extremely rarefied,After collision:,The change in momentum of the molecule,The time between collision is given by,The rate of momentum transfer from the molecule to the wall is,This is the force on the wall from the iths molecule,The momentum of the molecule before collision:,Each of the N molecules in the box has its own velocity, and therefore its own travel time and momentum transfer. For a single molecule, the force is intermittent , 单个分子:作用不连续; For the N molecules, the force per area is pressure 大量分子:作用连续 Summing over all the molecules in the box , the total rate of momentum transfer to the wall, and thus the force on the wall can be got:,Although the momentum transfer from a single molecule are intermittent, the total momentum transfer is a drumbeat of impulses that provides a steady push on the wall.,If the gas is not extremely rarefied, the molecule may collide with one another before completing the round trip. These collision turn out to conserve both momentum and kinetic energy, so the net impact on the wall is the same as if the particles had not collided with one another. Since the motion of the molecules is random, the contributions from the y and z components have the same value, it can be got :,The total force on the wall from all the molecules in the box,Review : (1) Idea 观点 (2) Method 方法,The pressure on the wall is the average force divided by the area,Conclusion As the random motion of the gas molecules becomes more vigorous, the average kinetic energy increases, resulting in correspondingly great pressure on the containing walls. Furthermore, a relationship between the macroscopic pressure and the microscopic average kinetic energy of the individual molecules of the gas can be found.,3 Temperature and energy,1 The relationship between average kinetic energy and temperature,On the other hand, studies of dependence of volume and pressure of an ideal gas on temperature suggest the ideal-gas law,The mean translational kinetic energy of an atom or molecule for ideal gas is directly proportional to the absolute temperature 理想气体的分子平均平动动能与绝对温度成正比 相同温度下,理想气体的分子平均平动动能均相等,This result means that temperature is evidence of disorganized motion of atom and molecules. 温度是气体热运动剧烈程度的标志 Temperature is the measure of hotness.,Question ：,分子平均平动动能相同的不同气体,温度是否相同？,Answer 同,2 Pressure formulas,3 Root-mean-square speed 方均根速率,Proportional to temperature Inversely proportional to molecular mass,大量分子的速率平方的平均值的 平方根,1 The degree of freedom 自由度,确定一个物体的空间位置所必需的独立坐标数目,A Freedom mass 自由质点,x y z,B freedom rigid body, x y z,4 Equipartition theorem of energy The internal energy of idea gas 能量均分定理 理想气体内能,x,y,z,i=3, ,i=6, ,2 The degree of freedom of molecules 分子的自由度, Monoatomic molecule 单原子分子:氦、氖、氩,i =3, Diatomic molecule 双原子分子:氢、氧、氮,哑铃,连线: 2个,质心:3个,i =5, Polyatomic molecule 多原子分子:（co2等),Translational degrees of freedom: 平动自由度: i平= 3 Rotational degrees of freedom: 转动自由度: i转= 3,i = i平 (3)+ i转(3)= 6,3 Equipartition theorem of energy 能量均分定理,在温度为T 的平衡态下，气体分子的每一自由度均有相同的平均动能 kT /2.,Monoatomic molecule i =3,3kT/2,Polyatomic molecule i =6 6kT/2=3kT,Diatomic molecule i =5 5kT/2,Notes:, 能量按自由度均分原理是统计性规律, 能量均分原理反映分子向各个方向运动的机会均等,4 Internal energy of ideal gas 理想气体的内能,Common gas,Ideal gas,One mole,Molar internal energy,Monoatomic molecule,Diatomic molecule:,Polyatomic molecule:,The internal energy of ideal gas is proportional to the temperature. 理想气体的内能与温度成正比,理想气体的内能是温度的单值函数,(1)机械能与内能有无区别？,(2)机械能与内能有无联系？,5 Maxwell speed distribution law 麦克斯韦分子速率分布定律,1 Maxwell speed distribution function,表示在某一速率区间 v v+v内分子数 占总分子数的百分比,表示分子速率在v 附近单位速率间隔内的分子数占总分子数的百分率,distribution function:,2 Physical meaning related physical quantities,(1),分子速率在 v 附近单位速率间隔内分子数占总分子数的百分率,（2）,分子速率在v - v +dv内的分子数占总分子数的百分比,（3）,vp,v,所有速率区间的分子数占总分子数的百分比为1,Most probable speed 最可几速率 vp,曲线峰值对应的速率,vp附近单位速率间隔内的分子数占总分子数的百分比最多,（4）,（5）,Most probable speed 最可几速率,Root-mean-square speed 方均根速率,Mean speed 平均速率,All of them are proportional to and,Ex. Calculate the rms speed of oxygen molecular at STP.,Solution,6 Mean collision frequency Mean free path,1 The physical meaning of,Mean collision frequency 平均碰撞次数,在平衡态下，单位时间内每个分子与其它分子相碰的平均次数,Mean free path 平均自由程,在平衡态下，分子连续两次碰撞之间所经过的自由路程的平均值,2 The expression of,Effective diameter,Number density,mean speed,大量气体分子作无规则的热运动，分子运动过程中将不断与其它分子碰