《E氣體動(dòng)理論》PPT課件.ppt

1、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

2、, 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

3、 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 microscopi

4、c 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 he

5、at 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,氣體動(dòng)理論和熱力學(xué)基礎(chǔ) The foundations of Gas kinetics and thermod

6、ynamics,1 研究對(duì)象,物質(zhì)的熱運(yùn)動(dòng)和熱運(yùn)動(dòng)與其它形式的運(yùn)動(dòng)之間相互轉(zhuǎn)化所遵循的規(guī)律,熱現(xiàn)象及其規(guī)律,組成宏觀物體的大量微觀粒子(分子、原子)的一種永不停息的無規(guī)則的運(yùn)動(dòng),熱運(yùn)動(dòng),熱現(xiàn)象,組成宏觀物體的大量微觀粒子熱運(yùn)動(dòng)的集體表現(xiàn),凡是與溫度有關(guān)的物理現(xiàn)象都是熱現(xiàn)象,熱運(yùn)動(dòng)是熱現(xiàn)象的微觀實(shí)質(zhì) 熱現(xiàn)象是熱運(yùn)動(dòng)的宏觀表現(xiàn),實(shí)例: 物體受熱溫度升高,體積膨脹,冰受熱融化為水等,2 研究方法,以物質(zhì)的分子、原子結(jié)構(gòu)概念和分子熱運(yùn)動(dòng)概念為基礎(chǔ), 將微觀運(yùn)動(dòng)和宏觀運(yùn)動(dòng)相聯(lián)系,應(yīng)用統(tǒng)計(jì)的方法,解釋并揭示物質(zhì)宏觀熱現(xiàn)象及其有關(guān)規(guī)律的本質(zhì),確立宏觀量和微觀量之間的關(guān)系系。 (1) 熱運(yùn)動(dòng) (2) 微觀量，

7、宏觀量 (3) 統(tǒng)計(jì)規(guī)律,Gas kinetics 氣體動(dòng)理論,1) 就整體而言, 在一定狀態(tài)下,物質(zhì)具有一定的能量; (2) 從一個(gè)狀態(tài)過度到另一個(gè)狀態(tài),遵從一定規(guī)律,Thermodynamics 熱力學(xué),不涉及物質(zhì)的微觀結(jié)構(gòu)，根據(jù)由觀察和實(shí)驗(yàn)總結(jié)得出的熱力學(xué)定律，從能量觀點(diǎn)出發(fā)，分析研究在物質(zhì)狀態(tài)變化過程中有關(guān)熱功轉(zhuǎn)化的關(guān)系和條件,Chapter 18 Gas kinetics,1 Equilibrium state Equation of state 2 Pressure formula for ideal gas 3 Temperature and Energy 4 Theorem o

8、f 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 平衡狀態(tài),Notes,Without external action (influence): Neither

9、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 熱動(dòng)平衡,無外界影響時(shí)宏觀性質(zhì)不隨時(shí)間變化的狀態(tài),1) Equilibrium state 平衡狀態(tài),2) State parameters 狀態(tài)參量 V P T,Volume

10、體積V,Temperature 溫度T,Pressure 壓強(qiáng)P,2 Equation of state of ideal gas 理想氣體狀態(tài)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 t

11、emperature 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 平衡狀態(tài),F(V P T)=0,Any object in thermaldynamicaal equilibrium are at the same temperature Thermodynamic

12、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

13、 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 -microscop

14、ic definition 理想氣體的分子模型-微觀定義,2 Pressure formula for ideal gas,The self size of molecules is far smaller than the average distance between molecules, being neglect 分子本身的線度遠(yuǎn)小于分子平均間距,可忽略不計(jì),2) The interactions between molecules and the wall of container are neglected except the instant of collisions 除碰撞

15、瞬間，忽略分子之間、分子與器壁之間的相互作用,3) The collisions between molecules and the wall of container are perfect elastic collisions 分子之間、分子與器壁之間的碰撞是完全彈性,2 The dominant idea 主導(dǎo)思想,1) Idea: 觀點(diǎn),Macroscopically 宏觀 Force per unit area,Microscopically 微觀 The constant, rapid drumbeat of molecules bouncing off the wall of t

16、he container exerts a steady average force on the wall,2) Method 方法,3) Result 結(jié)果,The average kinetic energy of a single molecule 一個(gè)分子的平均平動(dòng)動(dòng)能,n: Number density of molecules 分子數(shù)密度,Statistical method 統(tǒng)計(jì)方法,3 The derivation of pressure formula壓強(qiáng)公式的推導(dǎo),M,m,Gas is extremely rarefied,After collision,The chan

17、ge 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 therefo

18、re its own travel time and momentum transfer. For a single molecule, the force is intermittent , 單個(gè)分子:作用不連續(xù); For the N molecules, the force per area is pressure 大量分子:作用連續(xù) 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 b

19、e 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 collisio

20、n 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 t

21、he wall from all the molecules in the box,Review : (1) Idea 觀點(diǎn) (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

22、 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

23、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 理想氣體的分子平均平動(dòng)動(dòng)能與絕對(duì)溫度成正比 相同溫度下,理想氣體的分子平均平動(dòng)動(dòng)能均相等,This result means that temperatur

24、e is evidence of disorganized motion of atom and molecules. 溫度是氣體熱運(yùn)動(dòng)劇烈程度的標(biāo)志 Temperature is the measure of hotness,Question,分子平均平動(dòng)動(dòng)能相同的不同氣體,溫度是否相同,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

25、degree of freedom 自由度,確定一個(gè)物體的空間位置所必需的獨(dú)立坐標(biāo)數(shù)目,A Freedom mass 自由質(zhì)點(diǎn),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 理想氣體內(nèi)能,x,y,z,i=3,i=6,2 The degree of freedom of molecules 分子的自由度,Monoatomic molecule 單原子分子:氦、氖、氬,i =3,Diatomic molecule 雙原子分子:氫、氧、

26、氮,啞鈴,連線: 2個(gè),質(zhì)心:3個(gè),i =5,Polyatomic molecule 多原子分子:（co2等,Translational degrees of freedom: 平動(dòng)自由度: i平= 3 Rotational degrees of freedom: 轉(zhuǎn)動(dòng)自由度: i轉(zhuǎn)= 3,i = i平 (3)+ i轉(zhuǎn)(3)= 6,3 Equipartition theorem of energy 能量均分定理,在溫度為T 的平衡態(tài)下，氣體分子的每一自由度均有相同的平均動(dòng)能 kT /2,Monoatomic molecule i =3,3kT/2,Polyatomic molecule i =

27、6 6kT/2=3kT,Diatomic molecule i =5 5kT/2,Notes,能量按自由度均分原理是統(tǒng)計(jì)性規(guī)律,能量均分原理反映分子向各個(gè)方向運(yùn)動(dòng)的機(jī)會(huì)均等,4 Internal energy of ideal gas 理想氣體的內(nèi)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 temperat

28、ure. 理想氣體的內(nèi)能與溫度成正比,理想氣體的內(nèi)能是溫度的單值函數(shù),1)機(jī)械能與內(nèi)能有無區(qū)別,2)機(jī)械能與內(nèi)能有無聯(lián)系,5 Maxwell speed distribution law 麥克斯韋分子速率分布定律,1 Maxwell speed distribution function,表示在某一速率區(qū)間 v v+v內(nèi)分子數(shù) 占總分子數(shù)的百分比,表示分子速率在v 附近單位速率間隔內(nèi)的分子數(shù)占總分子數(shù)的百分率,distribution function,2 Physical meaning related physical quantities,1,分子速率在 v 附近單位速率間隔內(nèi)分子數(shù)占總

29、分子數(shù)的百分率,2,分子速率在v - v +dv內(nèi)的分子數(shù)占總分子數(shù)的百分比,3,vp,v,所有速率區(qū)間的分子數(shù)占總分子數(shù)的百分比為1,Most probable speed 最可幾速率 vp,曲線峰值對(duì)應(yīng)的速率,vp附近單位速率間隔內(nèi)的分子數(shù)占總分子數(shù)的百分比最多,4,5,Most probable speed 最可幾速率,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 平均碰撞次數(shù),在平衡態(tài)下，單位時(shí)間內(nèi)每個(gè)分子與其它分子相碰的平均次數(shù),Mean free path 平均自由程,在平衡態(tài)下，分子連續(xù)兩次碰撞之間所經(jīng)過的自由路程的平均值,2 The expression of,Effective diameter,Number density,mean speed,大量氣體分子作無規(guī)則的熱運(yùn)動(dòng)，分子運(yùn)