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7.1 «New proof of two theorems on the thermal equilibrium among gas molecules» (Wiener Berichte, 1887) 7.1 «New proof of two theorems on the thermal equilibrium among gas molecules» (Wiener Berichte, 1887)
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Lorentz’s critical argument Lorentz’s critical argument
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Boltzmann’s reaction Boltzmann’s reaction
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Comments Comments
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7.2 «On a few questions of the kinetic theory of gases» (Wiener Berichte and Philosophical Magazine, 1887) 7.2 «On a few questions of the kinetic theory of gases» (Wiener Berichte and Philosophical Magazine, 1887)
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Comments Comments
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7.3 «On the equilibrium of live force between progressive and rotational motion in gas molecules» (Berliner Berichte, 1888) 7.3 «On the equilibrium of live force between progressive and rotational motion in gas molecules» (Berliner Berichte, 1888)
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Burnside’s calculation Burnside’s calculation
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Boltzmann’s reply Boltzmann’s reply
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Comments Comments
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7.4 «Van’t Hoff’s hypothesis on the osmotic pressure from the point of view of the kinetic theory of gases» (Zeitschrift für physikalische Chemie, 1890) «Postscript to the consideration of van’t Hoff’s hypothesis from the point of view of the kinetic theory of gases» (Zeitschrift für physikalische Chemie, 1891) 7.4 «Van’t Hoff’s hypothesis on the osmotic pressure from the point of view of the kinetic theory of gases» (Zeitschrift für physikalische Chemie, 1890) «Postscript to the consideration of van’t Hoff’s hypothesis from the point of view of the kinetic theory of gases» (Zeitschrift für physikalische Chemie, 1891)
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Van’t Hoff’s analogy between solutes and gases Van’t Hoff’s analogy between solutes and gases
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Boltzmann’s kinetic-theoretical derivation Boltzmann’s kinetic-theoretical derivation
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Lorentz’s criticism Lorentz’s criticism
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Comments Comments
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7.5 «Studies on the equilibrium of live force. Part III» (Münchener Berichte and Philosophical Magazine, 1892) 7.5 «Studies on the equilibrium of live force. Part III» (Münchener Berichte and Philosophical Magazine, 1892)
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Kelvin’s test cases Kelvin’s test cases
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Boltzmann’s reply Boltzmann’s reply
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Kelvin’s “decisive test-case” Kelvin’s “decisive test-case”
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Comments Comments
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7.6 «On a note by Mr. Hans Cornelius regarding the ratio of the energies of translational and internal motion of gas molecules» (Zeitschrift für physikalische Chemie, 1893) 7.6 «On a note by Mr. Hans Cornelius regarding the ratio of the energies of translational and internal motion of gas molecules» (Zeitschrift für physikalische Chemie, 1893)
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7.7 «On Maxwell’s method of deriving the equations of hydrodynamics from the kinetic theory of gases» (British Association report, 1894) 7.7 «On Maxwell’s method of deriving the equations of hydrodynamics from the kinetic theory of gases» (British Association report, 1894)
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7.8 «On the application of the determinantal relation to the kinetic theory of polyatomic gases» (British Association report, 1894) 7.8 «On the application of the determinantal relation to the kinetic theory of polyatomic gases» (British Association report, 1894)
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Bryan’s report Bryan’s report
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Boltzmann’s new derivation Boltzmann’s new derivation
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Comments Comments
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7.9 «On the mechanical analogue of thermal equilibrium between bodies in contact» (with George Bryan, Wiener Berichte, 1894, and Proceedings of the London Physical Society, 1895) 7.9 «On the mechanical analogue of thermal equilibrium between bodies in contact» (with George Bryan, Wiener Berichte, 1894, and Proceedings of the London Physical Society, 1895)
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Comments Comments
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7.10 «On the proof of Maxwell’s distribution of velocities among molecules» (Münchener Berichte, Annalen der Physik, 1894) «More on Maxwell’s velocity distribution» (Münchener Berichte, Annalen der Physik, 1895) 7.10 «On the proof of Maxwell’s distribution of velocities among molecules» (Münchener Berichte, Annalen der Physik, 1894) «More on Maxwell’s velocity distribution» (Münchener Berichte, Annalen der Physik, 1895)
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Kirchhoff’s derivation Kirchhoff’s derivation
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Boltzmann’s reaction Boltzmann’s reaction
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Planck’s reply Planck’s reply
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Boltzmann’s reply Boltzmann’s reply
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Comments Comments
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7 Consolidation (1887–1895)
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Published:February 2018
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Abstract
This chapter covers a period in which Boltzmann returned to the collision-based approach and consolidated it in answer to criticism and suggestions by William Thomson, Hendrik Lorentz, George Bryan, Gustav Kirchhoff, and Max Planck. He corrected errors in alleged counterexamples of equipartition by William Burnside and William Thomson; and in 1887, when the Dutch theorist Hendrik Lorentz detected an error in his earlier derivation of the H theorem for polyatomic gases, he devised a highly ingenious alternative. In 1894, he offered a new, simplified derivation of the Maxwell–Boltzmann distribution based on an idea by the British mathematician George Bryan. Together with Bryan, he also provided a kinetic-molecular model for the equalization of the temperatures of two contiguous gases. He denounced what he believed to be an error in Gustav Kirchhoff’s derivation of Maxwell’s distribution, and he strengthened Max Planck’s alternative derivation based on time reversal.
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