*Olivier Darrigol*

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198816171
- eISBN:
- 9780191853661
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198816171.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics, History of Physics

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, ...
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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.Less

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.

*Olivier Darrigol*

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198816171
- eISBN:
- 9780191853661
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198816171.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics, History of Physics

This chapter is the first subset of a set of critical summaries Boltzmann’s writings on kinetic-molecular theory. It covers a first period in which he tried to construct the laws of thermal ...
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This chapter is the first subset of a set of critical summaries Boltzmann’s writings on kinetic-molecular theory. It covers a first period in which he tried to construct the laws of thermal equilibrium, including the existence of the entropy function and the Maxwell–Boltzmann law, by various means including the principle of least action, Maxwell’s collision formula, the ergodic hypothesis, and a procedure of adiabatic variation. This is an immensely fertile period in which Boltzmann introduced several of the basic concepts, problems, and difficulties of modern statistical mechanics.Less

This chapter is the first subset of a set of critical summaries Boltzmann’s writings on kinetic-molecular theory. It covers a first period in which he tried to construct the laws of thermal equilibrium, including the existence of the entropy function and the Maxwell–Boltzmann law, by various means including the principle of least action, Maxwell’s collision formula, the ergodic hypothesis, and a procedure of adiabatic variation. This is an immensely fertile period in which Boltzmann introduced several of the basic concepts, problems, and difficulties of modern statistical mechanics.

*Robert T. Hanlon*

- Published in print:
- 2020
- Published Online:
- April 2020
- ISBN:
- 9780198851547
- eISBN:
- 9780191886133
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851547.003.0041
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Maxwell produced two publications on the kinetic theory of gases in which he proposed his eponymous velocity distribution of velocities, his theory on the equipartition of energy, and finally his ...
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Maxwell produced two publications on the kinetic theory of gases in which he proposed his eponymous velocity distribution of velocities, his theory on the equipartition of energy, and finally his famed transport equations. In this work he surprisingly predicted that gas viscosity is independent of density and then confirmed this finding in experiments he conducted with his wife.Less

Maxwell produced two publications on the kinetic theory of gases in which he proposed his eponymous velocity distribution of velocities, his theory on the equipartition of energy, and finally his famed transport equations. In this work he surprisingly predicted that gas viscosity is independent of density and then confirmed this finding in experiments he conducted with his wife.