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1、第三章 输运现象与分子动理学理论的非平衡态理论The third chapter is non-equilibrium theory of transport phenomena and molecular dynamics theory3-1 hydrogen in the mean free path, the * m, the effective diameter for the hydrogen molecule.Solution: by = = get:= substituting data: (m)The effective diameter of 3-2 nitrogen mol
2、ecules, the average time for the standard condition and the mean free path of two consecutive collisions between.Solution = = substituting data - - (m)= substituting data:= (s)The effective diameter of 3-3 oxygen molecule is 3.6 * m, and the collision frequency is calculated,Known: (1) the temperatu
3、re of oxygen is 300K, the pressure is 1.0atm;(2) the oxygen temperature is 300K, and the pressure is 1 * ATMSolution: by = = = substituting data:= 6.3 * ()()Some 3-4 gas molecular mean free path in the.(1) the effective diameter of the known molecule is the pressure of the gas.(2) calculate the numb
4、er of collisions with other molecules on the path of the molecule.Solution: (1) from:Substituting data:(2) the number of molecular walk collisions(second)If in the next 3-5, the mean free path for what in the molecular itch, pressure, the mean free path for? Let the temperature remain the same.Solut
5、ion: fromBesides the vacuum tube is about HG, the effective diameter set of gas molecules, the number of molecules per unit volume, mean free path and collision frequency.Solution:(2)(3) if there is air in the tube, thenThe measured temperature is 3-7 pressure too, the mean free path of argon and ne
6、on molecules respectively and asked:(1) what is the ratio of the effective diameter of the argon molecule to that of the neon molecule?(2) how old is it?(3) how old is it?Solution: (1) from:(2) assume that argon molecules are equally effective in two states:(3) a neon gas molecules in two is effecti
7、ve under the condition of equal diameter, and (2) similarly to:In a gas discharge tube 3-8, electronic collision with the gas molecular phase, because the electronic rate is far greater than the average rate of gas molecules, so the latter can be considered stationary. The effective diameter of the
8、electron is negligible compared to the effective diameter of the gas molecule.(1) what is the collision cross section between the electron and the gas molecule?(2) it is proved that the average free range of electron collisions with gas molecules is: n is the number density of gas molecules.Solution
9、: (1) because the effective diameter of an electron is negligible compared to the effective diameter of a gas molecule, electrons can be regarded as particles. Because the gas molecules can be regarded as relatively static, so where the center from the electronic distance equal to or less than the m
10、olecular energy and electronic collide, and collision cross section:(2) the collision frequency between electron and gas molecule is:(for electron average rate)3-9 the average free path of a gas molecule is proved to be the probability that a molecule travels at least x for two consecutive collision
11、sSolution: (4.6) according to the ratio of molecular formula in a molecule in free path is greater than X of the total number of molecules is known by chance = concept: for a molecule, risk free path is greater than x, so a two consecutive molecular collision probability of at least x walking distan
12、ce is.The mean free path of gas molecules is a 3-10 10cm, in the 10000 section of free process, (1) the number of period is longer than 10cm? (2) how many segments are longer than 50cm? (3) how many segments are longer than 5cm and shorter than 10cm? (4) how many segments are between 9.9cm and 10cm?
13、 (5) how many segments are just 10cm in length?Solution: according to the different distribution of free path of molecular molecular number in the ratio of the total number of molecules with the same probability of a molecule in different free path distribution in free process, with the molecular fr
14、ee path in a free path that a number of molecules is free in the process of the number of. soThe number of segments in which the free path is longer than x(1) the number of segments longer than 10cm, and the total number of segments is= (paragraph)(2) the number of segments longer than 50cm is= (par
15、agraph)(3) the number of segments shorter than 10cm is longer than 5cm(paragraph)(4) the number of segments between 9.9cm and 10cm is set as(paragraph)(5) according to the laws of statistics, it is not certain how many lengths are exactly 10cm.A moment of 3-11 has a set of oxygen molecules and other
16、 molecular collision just after, ask how much time after the left half not with other molecules collide. The oxygen molecules move at an average rate, and the oxygen temperature is 300K. At a given pressure, the average free range of oxygen molecules is 2.0cm.Solution: considering the molecular dist
17、ance traveled by X in t time, the number of molecules not touched is equal to the number of molecules in the total number of molecules whose free range is greater than x. The number of molecules with a free range greater than x is N(s)The 3-12 cathode ray tube pumped high vacuum (mmHg), in order to
18、ensure that the electrons emitted from the cathode anode 90% can reach 20cm in the distance, but not in the middle of collide with air molecules?Solution: the electron emitted from the cathode has an electron with a free range greater than 20cm, and there are NKnow by the eighth chapter of this chap
19、ter:If the temperature is so, the main component of the air is nitrogen, so the approximate value of the effective diameter of the air molecule is obtained by thermal example 1:Substituting data:Gas 3-13 by the electron gun emits a beam of electron injection pressure for the. A collecting electrode
20、of the electron gun before in the distance of X, used for the determination of free (i.e. not by gas molecules collide with electrons in the distance). The intensity of the electron stream emitted by the electron gun is (1). When the pressure is x = 10cm, the intensity of the electron stream reachin
21、g the collector is. (1) what is the average free range of electrons? (2) when the pressure drops, how large is the electron flow to the collector?Solution: because the electron flow intensity is proportional to the electron number, so there is the electron flow intensity caused by the electron at th
22、e collector in the free range greater than x.(1)(2) from the above question:Well:3-14 the hysteresis coefficient of nitrogen measured at this time is calculated as the effective diameter of nitrogen molecule, and the molecular weight of nitrogen is 28.Solution: by the heat (4.18) known:Substituting
23、data:3-15 the heat conductivity of nitrogen is measured at this time, and the constant volume molar heat capacity is as follows: the effective diameter of nitrogen molecule is calculatedExplanation: from heat (4.19)Substituting numbers:The diffusion coefficient of oxygen in 3-16 under standard condi
24、tions:The average free path of oxygen molecules.Solution:Substituting dataThe atomic weight of 3 - 17 known helium and argon are respectively 4 and 40, their viscosity in standard dia respectively and requirements: (1) and argon helium molecule collision cross section ratio of argon and helium; (2)
25、the thermal conductivity ratio; (3) the diffusion coefficient of argon the ratio of helium.Solution: known(1) on the basis of(2) because the nitrogen and argon are monatomic molecules, the molar heat capacity is the same as that of C(3) now P and T are the same,3 - 18 a length of 2m, the cross secti
26、onal area of the pipe stored under standard conditions, half molecule of C atom is a radioactive isotope, when radioactive molecules in dense tube left, the molecular number density along the tube uniformly decreases to the right end is reduced to zero. (1) what is the density gradient of radioactiv
27、e gas at the beginning? (2) at the beginning, the number of radioactive molecules per second from left to right through the midpoint of the cross section of the tubes? (3) how many from the right to the left? (4) how many grams of radioactive gas are diffused per second through the cross section of
28、the pipe at the beginning?Solution: known tube length L = 2.0m, cross-sectional area(1) from the beginning and the end of the question, all the molecules are radioactive. The unit volume is n, while the right end is zero. Radioactive gas density gradient:The number of molecules per unit volume of a
29、gas under standard conditions:(2) according to the microscopic explanation of diffusion phenomena, the number of molecules moving from left to right in mid time through midpoint DS isN medium Chinese DSDTRefer to the thermodynamic (table 4-1), desirable cm. Because the tube is very small, can be ass
30、umed constant at the beginning of second approximation, in seconds from the left to the right end surface by S molecular numberSubstituting data(unit)(3) similarly available within one second from the right end of the surface to the left side of the S radioactive molecular number:(unit)(4) the numbe
31、r of radioactive molecules that diffuse through the S surface per second(unit)The quality of radioactive gas passing through the S surface per second3-19, a cylinder is hung along the shaft on the wire, and a cylindrical cylinder is placed outside the cylinder, which is filled with air. When the cyl
32、inder rotates at a certain angular speed, the cylinder will be subjected to a force distance due to the hysteresis of the air, and the force distance can be determined by the degree of torsion of the suspension wire, thus the coefficient of hysteresis of the air can be obtained. The radius of the cy
33、linder is R, and the radius of the cylinder is both. The length of the cylinder is L, and the angular velocity of the cylinder is. It is proved that it is the hysteresis coefficient to be measured.It is proved that the force of interaction between gas and cylinder is:In the case of equilibrium only,
34、 the cylinder can be approximately stationary, and the rotation speed of the cylinder is:The velocity of the molecules adjacent to the cylinder is the same as that of the cylinderBy Newtons law of hysteresis, the hysteresis force of a cylinder is observedLateral area of cylinder3 - 20 two 100cm long
35、 radius, respectively 10.0cm and 10.5cm coaxial cylinder set together, which is full of hydrogen, hydrogen if the lag coefficient is James, asked how much of the outer cylinder speed when the inner cylinder can make real force by 107dyn?Solution: the result of the above question:amongbeSubstituting
36、data is: (radians / sec)3 - 21 two total long cylinder sleeve together, two cylinder length is L, the radius of the inner cylinder and the outer cylinder respectively, the inner cylinder and the outer cylinder are maintained at constant temperature and, and two of the air cylinder, the known thermal
37、 conductivity is K, it is shown that: per second by the inner tube through the air to the outer cylinder of the heat:Proof: by the laws of the interior of the blade:In the unit time, the heat of a cylinder with a radius of R is used as:It is a constant, and due to the surface by heat is a constant, so the ends of the integral type: