复旦大学：《大学物理——热学》课程教学资源（PPT课件）第7次课

大学物理(热学) 金晓峰 复旦大学物理系 xfin@fudan.edu.cn ftp:/10.45.8888大学物理06xfin 2006-9-30 2021/9/5

2021/9/5 1 大学物理（热学） 金晓峰 复旦大学物理系 xfjin@fudan.edu.cn ftp://10.45.88.88/大学物理06xfjin 2006-9-30

1913, Planck, Nernst, Rubens, and Warburg proposed Einstein for Prussian Academy 6... That he may sometimes have missed the target in his speculations, as for example, in his hypothesis of light quanta cannot really be held too much against him, for it is not possible to introduce fundamentally new ideas, even in the most exact sciences, without occasionally taking a risk

“ … That he may sometimes have missed the target in his speculations, as for example, in his hypothesis of light quanta , cannot really be held too much against him, for it is not possible to introduce fundamentally new ideas, even in the most exact sciences, without occasionally taking a risk. ” 1913, Planck, Nernst, Rubens, and Warburg proposed Einstein for Prussian Academy:

James Clark Maxwell It is of great advantage to the student of any subject to read the origina memoirs on that subject for science is always most completely assimilated when it is in the nascent state

It is of great advantage to the student of any subject t o r e a d t h e o r i g i n a l memoirs on that subject, for science is always most completely assimilated when it is in the nascent state. James Clark Maxwell

James Clark Maxwell 对任何领域的学生来说 阅读相关的原始文献都是极 有益处的,因为处在雏形中 的科学最容易被消化

对任何领域的学生来说， 阅读相关的原始文献都是极 有益处的，因为处在雏形中 的科学最容易被消化。 James Clark Maxwell

MAXWELL: THE DYNAMICAL THEORY OF GASES Phil Mag. 19(1860)19153 Let n be the whole number of particles. Let x, y, z be the com- ponents of the velocity of each particle in three rectangular direc- tions,and let the number of particles for which x lies between x and x+ dx, be Nf(x)dx, where f(x) is a function of x to be determined The number of particles for which y lies between y and y+ dy will be Nfdy; and the number for which z lies between z and z dz will be Nf(z)dz, where f always stands for the same function Now the existence of the velocity x does not in any way affect that of the velocities y or z, since these are all at right angles to each other and independent, so that the number of particles whose velocity lies between x and x dx, and also between y and y t dy, and also between z and z dz, is M(x)0)(2kx劬d If we suppose the N particles to start from the origin at the same instant, then this will be the number in the element of volume (dx dy dz) after unit of time, and the number referred to unit of volume will be Nf(fo)f(z)

Phil. Mag. 19 (1860) 19

But the directions of the coordinates are perfectly arbitrary, and therefore this number must depend on the distance from the origin alone, that is f(x))f(z)=(x2+y2+z2) Solving this functional equation, we find f(e C d(r2) If we make A positive, the number of particles will increase with the velocity, and we should find the whole number of particles infinite. We therefore make A negative and equal to- 1/, so that the number between x and x+ dx is NCe-la)dx Integrating from x=-oo to x =+oo, we find the whole number of particles, Nvzx=M,∴C≈、l av兀

l54 SELECTED READINGS IN PHYSICS. KINETIC THEORY f(r)is therefore (ra) v Whence we may draw the following conclusions: Ist. The number of particles whose velocity, resolved in a certain direction, lies between x and x + dx is N v 2nd. The number whose actual velocity lies between u and u t du 4 N v2e-(o/adu 3rd. To find the mean value of D, add the velocities of all the particles together and divide by the number of particles; the result is mean velocity 4th. To find the mean value of u2, add all the values together and divide by N mean value of v This is greater than the square of the mean velocity, as it ougl

FIGURE 18-2 Distribution of speeds of molecules in an ideal gas Note that v and vrms are not at the peak of the curve(that speed is called the“ most probable speed,” Up). This is because the curve is skewed to the right: it is not symmetrical 9 8 0 prm Speed v

麦克斯韦分布演示 程序

麦克斯韦分布演示 • 程序

R D L V Pump FIGURE 22-8. Apparatus used by Miller and Kusch to verify the Maxwell speed distribution. A beam of thallium molecules leaves the oven O through the slit S, travels through the helical groove in the rotating cylinder R, and strikes the detector D. The angular velocity w of the cylinder can be varied so that molecules of differing speeds will pass through the cylinder