Lectures on Gas Theory

Ludwig Boltzmann

Book

Lectures on Gas Theory

Ludwig Boltzmann
Edited by: Stephen G. Brush

Language: English

Published/Copyright: 2023

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This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

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Engineering Mechanical Engineering Thermodynamics

Frontmatter Publicly Available Download PDF	I
CONTENTS Publicly Available Download PDF	V
Translator's Introduction Requires Authentication Unlicensed Licensed Download PDF	1
PART I THEORY OF GASES WITH MONATOMIC MOLECULES, WHOSE DIMENSIONS ABE NEGLIGIBLE COMPARED TO THE MEAN FREE PATH
NOTE ON LITERATURE CITATIONS Requires Authentication Unlicensed Licensed Download PDF	20
Foreword Requires Authentication Unlicensed Licensed Download PDF	21
Introduction Requires Authentication Unlicensed Licensed Download PDF	23
1. Mechanical analogy for the behavior of a gas Requires Authentication Unlicensed Licensed Download PDF	23
2. Calculation of the pressure of a gas Requires Authentication Unlicensed Licensed Download PDF	30
CHAPTER I THE MOLECULES ARE ELASTIC SPHERES. EXTERNAL FORCES AND VISIBLE MASS MOTION ABE ABSENT Requires Authentication Unlicensed Licensed Download PDF	36
3. Maxwell's proof of the velocity distribution law; frequency of collisions Requires Authentication Unlicensed Licensed Download PDF	36
4. Continuation; values of the variables after the collision; collisions of the opposite kind Requires Authentication Unlicensed Licensed Download PDF	43
5. Proof that Maxwell's velocity distribution is the only possible one Requires Authentication Unlicensed Licensed Download PDF	49
6. Mathematical meaning of the quantity H Requires Authentication Unlicensed Licensed Download PDF	55
7. The Boyle-Charles-Avogadro law. Expression for the heat supplied Requires Authentication Unlicensed Licensed Download PDF	62
8. Specific heat. Physical meaning of the quantity H Requires Authentication Unlicensed Licensed Download PDF	68
9. Number of collisions Requires Authentication Unlicensed Licensed Download PDF	75
10. Mean free path Requires Authentication Unlicensed Licensed Download PDF	82
11. Basic equation for the transport of any quantity by the molecular motion Requires Authentication Unlicensed Licensed Download PDF	87
12. Electrical conduction and viscosity of the gas Requires Authentication Unlicensed Licensed Download PDF	91
13. Heat conduction and diffusion of the gas Requires Authentication Unlicensed Licensed Download PDF	98
14. Two kinds of approximations; diffusion of two different gases Requires Authentication Unlicensed Licensed Download PDF	104
CHAPTER II THE MOLECULES ABE CENTERS OF FORCE. CONSIDERATION OF EXTERNAL FORCES AND VISIBLE MOTIONS OF THE GAS Requires Authentication Unlicensed Licensed Download PDF	110
15. Development of partial differential equations for f and F Requires Authentication Unlicensed Licensed Download PDF	110
16. Continuation. Discussion of the effects of collisions Requires Authentication Unlicensed Licensed Download PDF	114
17. Time-derivatives of sums over all molecules in a region Requires Authentication Unlicensed Licensed Download PDF	123
18. More general proof of the entropy theorem. Treatment of the equations corresponding to the stationary state Requires Authentication Unlicensed Licensed Download PDF	131
19. Aerostatics. Entropy of a heavy gas whose motion does not violate Equations (147) Requires Authentication Unlicensed Licensed Download PDF	141
20. General form of the hydrodynamic equations Requires Authentication Unlicensed Licensed Download PDF	147
CHAPTER III THE MOLECULES REPEL EACH OTHER WITH A FORCE INVERSELY PROPORTIONAL TO THE FIFTH POWER OF THEIR DISTANCE Requires Authentication Unlicensed Licensed Download PDF	161
21. Integration of the terms resulting from collisions Requires Authentication Unlicensed Licensed Download PDF	161
22. Relaxation time. Hydrodynamic equations corrected for viscosity. Calculation of Bb using spherical functions Requires Authentication Unlicensed Licensed Download PDF	172
23. Heat conduction. Second method of approximate calculations Requires Authentication Unlicensed Licensed Download PDF	182
24. Entropy for the case when Equations (147) are not satisfied. Diffusion Requires Authentication Unlicensed Licensed Download PDF	197
PART II VAN DER WAALS' THEORY; GASES WITH COMPOUND MOLECULES; GAS DISSOCIATION ; CONCLUDING REMARKS
Foreword Requires Authentication Unlicensed Licensed Download PDF	215
CHAPTER I FOUNDATIONS OF VAN DER WAALS' THEORY Requires Authentication Unlicensed Licensed Download PDF	217
1. General viewpoint of van der Waals Requires Authentication Unlicensed Licensed Download PDF	217
2. External and internal pressure Requires Authentication Unlicensed Licensed Download PDF	220
3. Number of collisions against the wall Requires Authentication Unlicensed Licensed Download PDF	221
4. Relation between molecular extension and collision number Requires Authentication Unlicensed Licensed Download PDF	222
5. Determination of the impulse imparted to the molecules Requires Authentication Unlicensed Licensed Download PDF	224
6. Limits of validity of the approximations made in §4 Requires Authentication Unlicensed Licensed Download PDF	226
7. Determination of internal pressure Requires Authentication Unlicensed Licensed Download PDF	227
8. An ideal gas as a thermometric substance Requires Authentication Unlicensed Licensed Download PDF	230
9. Temperature-pressure coefficient. Determination of the constants of van der Waals' equation Requires Authentication Unlicensed Licensed Download PDF	231
10. Absolute temperature. Compression coefficient Requires Authentication Unlicensed Licensed Download PDF	234
11. Critical temperature, critical pressure, and critical volume Requires Authentication Unlicensed Licensed Download PDF	236
12. Geometric discussion of the isotherms Requires Authentication Unlicensed Licensed Download PDF	240
13. Special cases Requires Authentication Unlicensed Licensed Download PDF	243
CHAPTER II PHYSICAL DISCUSSION OF THE VAN DER WAALS' THEORY Requires Authentication Unlicensed Licensed Download PDF	246
14. Stable and unstable states Requires Authentication Unlicensed Licensed Download PDF	246
15. Undercooling. Delayed evaporation Requires Authentication Unlicensed Licensed Download PDF	248
16. Stable coexistence of both phases Requires Authentication Unlicensed Licensed Download PDF	250
17. Geometric representation of the states in which two phases coexist Requires Authentication Unlicensed Licensed Download PDF	253
18. Definition of the concepts gas, vapor, and liquid Requires Authentication Unlicensed Licensed Download PDF	256
19. Arbitrariness of the definitions of the preceding section Requires Authentication Unlicensed Licensed Download PDF	257
20. Isopycnic changes of state Requires Authentication Unlicensed Licensed Download PDF	259
21. Calorimetry of a substance following van der Waals' law Requires Authentication Unlicensed Licensed Download PDF	261
22. Size of the molecule Requires Authentication Unlicensed Licensed Download PDF	264
23. Relations to capillarity Requires Authentication Unlicensed Licensed Download PDF	265
24. Work of separation of the molecules Requires Authentication Unlicensed Licensed Download PDF	268
CHAPTER III PRINCIPLES OF GENERAL MECHANICS NEEDED FOR GAS THEORY Requires Authentication Unlicensed Licensed Download PDF	271
25. Conception of the molecule as a mechanical system characterized by generalized coordinates Requires Authentication Unlicensed Licensed Download PDF	271
26. Liouville's Theorem Requires Authentication Unlicensed Licensed Download PDF	274
27. On the introduction of new variables in a product of differentials Requires Authentication Unlicensed Licensed Download PDF	278
28. Application to the formulas of §26 Requires Authentication Unlicensed Licensed Download PDF	283
29. Second proof of Liouville's theorem Requires Authentication Unlicensed Licensed Download PDF	285
30. Jacobi's theorem of the last multiplier Requires Authentication Unlicensed Licensed Download PDF	290
31. Introduction of the energy differential Requires Authentication Unlicensed Licensed Download PDF	294
32. Ergoden Requires Authentication Unlicensed Licensed Download PDF	297
33. Concept of the momentoid Requires Authentication Unlicensed Licensed Download PDF	300
34. Expression for the probability; average values Requires Authentication Unlicensed Licensed Download PDF	304
35. General relationship to temperature equilibrium Requires Authentication Unlicensed Licensed Download PDF	310
CHAPTER IV GASES WITH COMPOUND MOLECULES Requires Authentication Unlicensed Licensed Download PDF	313
36. Special treatment of compound molecules Requires Authentication Unlicensed Licensed Download PDF	313
37. Application of Kirchhoff's method to gases with compound molecules Requires Authentication Unlicensed Licensed Download PDF	315
38. On the possibility that the states of a very large number of molecules can actually lie within very narrow limits Requires Authentication Unlicensed Licensed Download PDF	317
39. Treatment of collisions of two molecules Requires Authentication Unlicensed Licensed Download PDF	319
40. Proof that the distribution of states assumed in §37 will not be changed by collisions Requires Authentication Unlicensed Licensed Download PDF	323
41. Generalizations Requires Authentication Unlicensed Licensed Download PDF	325
42. Mean value of the kinetic energy corresponding to a momentoid Requires Authentication Unlicensed Licensed Download PDF	327
43. The ratio of specific heats, K Requires Authentication Unlicensed Licensed Download PDF	331
44. Value of k for special cases Requires Authentication Unlicensed Licensed Download PDF	332
45. Comparison with experiment Requires Authentication Unlicensed Licensed Download PDF	334
46. Other mean values Requires Authentication Unlicensed Licensed Download PDF	336
47. Treatment of directly interacting molecules Requires Authentication Unlicensed Licensed Download PDF	338
CHAPTER V DERIVATION OF VAN DER WAALS' EQUATION BY MEANS OF THE VIRIAL CONCEPT Requires Authentication Unlicensed Licensed Download PDF	341
48. Specification of the point at which van der Waals' mode of reasoning requires improvement Requires Authentication Unlicensed Licensed Download PDF	341
49. More general concept of the virial Requires Authentication Unlicensed Licensed Download PDF	342
50. Virial of the external pressure acting on a gas Requires Authentication Unlicensed Licensed Download PDF	344
51. Probability of finding the centers of two molecules at a given distance Requires Authentication Unlicensed Licensed Download PDF	346
52. Contribution to the virial resulting from the finite extension of the molecules Requires Authentication Unlicensed Licensed Download PDF	350
53. Virial of the van der Waals cohesion force Requires Authentication Unlicensed Licensed Download PDF	352
54. Alternatives to van der Waals' formulas Requires Authentication Unlicensed Licensed Download PDF	354
55. Virial for any arbitrary law of repulsion of the molecules Requires Authentication Unlicensed Licensed Download PDF	356
56. The principle of Lorentz's method Requires Authentication Unlicensed Licensed Download PDF	358
57. Number of collisions Requires Authentication Unlicensed Licensed Download PDF	361
58. More exact value of the mean free path. Calculation of W/ according to Lorentz's method Requires Authentication Unlicensed Licensed Download PDF	364
59. More exact calculation of the space available for the center of a molecule Requires Authentication Unlicensed Licensed Download PDF	365
60. Calculation of the pressure of the saturated vapor from the laws of probability Requires Authentication Unlicensed Licensed Download PDF	367
61. Calculation of the entropy of a gas satisfying van der Waals' assumptions, using the calculus of probabilities Requires Authentication Unlicensed Licensed Download PDF	370
CHAPTER VI THEORY OF DISSOCIATION Requires Authentication Unlicensed Licensed Download PDF	376
62. Mechanical picture of the chemical affinity of monovalent similar atoms Requires Authentication Unlicensed Licensed Download PDF	376
63. Probability of chemical binding of an atom with a similar one Requires Authentication Unlicensed Licensed Download PDF	379
64. Dependence of the degree of dissociation on pressure Requires Authentication Unlicensed Licensed Download PDF	383
65. Dependence of the degree of dissociation on temperature Requires Authentication Unlicensed Licensed Download PDF	385
66. Numerical calculations Requires Authentication Unlicensed Licensed Download PDF	389
67. Mechanical picture of the affinity of two dissimilar monovalent atoms Requires Authentication Unlicensed Licensed Download PDF	393
68. Dissociation of a molecule into two heterogeneous atoms Requires Authentication Unlicensed Licensed Download PDF	396
69. Dissociation of hydrogen iodide gas Requires Authentication Unlicensed Licensed Download PDF	398
70. Dissociation of water vapor Requires Authentication Unlicensed Licensed Download PDF	399
71. General theory of dissociation Requires Authentication Unlicensed Licensed Download PDF	402
72. Relation of this theory to that of Gibbs Requires Authentication Unlicensed Licensed Download PDF	406
73. The sensitive region is uniformly distributed around the entire atom Requires Authentication Unlicensed Licensed Download PDF	408
CHAPTER VII SUPPLEMENTS TO THE LAWS OF THERMAL EQUILIBRIUM IN GASES WITH COMPOUND MOLECULES Requires Authentication Unlicensed Licensed Download PDF	412
74. Definition of the quantity H, which measures the probabilities of states Requires Authentication Unlicensed Licensed Download PDF	412
75. Change of the quantity H through intramolecular motion Requires Authentication Unlicensed Licensed Download PDF	414
76. Characterization of the first special case considered Requires Authentication Unlicensed Licensed Download PDF	415
77. Form of Liouville's theorem in the special case considered Requires Authentication Unlicensed Licensed Download PDF	417
78. Change of the quantity if as a consequence of collisions Requires Authentication Unlicensed Licensed Download PDF	419
79. Most general characterization of the collision of two molecules Requires Authentication Unlicensed Licensed Download PDF	422
80. Application of Liouville's theorem to collisions of the most general kind Requires Authentication Unlicensed Licensed Download PDF	424
81. Method of calculation with finite differences Requires Authentication Unlicensed Licensed Download PDF	427
82. Integral expression for the most general change of H by collisions Requires Authentication Unlicensed Licensed Download PDF	431
83. Detailed specification of the case now to be considered Requires Authentication Unlicensed Licensed Download PDF	432
84. Solution of the equation valid for each collision Requires Authentication Unlicensed Licensed Download PDF	433
85. Only the atoms of a single type collide with each other Requires Authentication Unlicensed Licensed Download PDF	435
86. Determination of the probability of a particular kind of central motion Requires Authentication Unlicensed Licensed Download PDF	437
87. Characterization of our assumption about the initial state Requires Authentication Unlicensed Licensed Download PDF	441
88. On the return of a system to a former state Requires Authentication Unlicensed Licensed Download PDF	443
89. Relation to the second law of thermodynamics Requires Authentication Unlicensed Licensed Download PDF	444
90. Application to the universe Requires Authentication Unlicensed Licensed Download PDF	446
91. Application of the probability calculus in molecular physics Requires Authentication Unlicensed Licensed Download PDF	448
92. Derivation of thermal equilibrium by reversal of the time direction Requires Authentication Unlicensed Licensed Download PDF	450
93. Proof for a cyclic series of a finite number of states Requires Authentication Unlicensed Licensed Download PDF	453
BIBLIOGRAPHY Requires Authentication Unlicensed Licensed Download PDF	454
INDEX Requires Authentication Unlicensed Licensed Download PDF	483

Publishing information

Pages and Images/Illustrations in book

eBook published on:

November 15, 2023

eBook ISBN:

9780520327474

Edition:

Reprint 2020

Pages and Images/Illustrations in book

Main content:

500

Other:

1 frontisp.

https://doi.org/10.1525/9780520327474

eBook ISBN: 9780520327474

Keywords for this book

calorimetry; kinetic theory; physics; thermodynamics

Lectures on Gas Theory

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