Abstract
Random motion of particles, so well put into words by Lucretius in Sect. 2.5, was quantified by the kinetic theory of matter in the second half of the nineteenth century. As we have seen in Chap. 2, this theory eventually lead to the demasking of Brownian movements as an instance of thermal motion, be it a remarkable instance, that can be observed with microscopy on colloids dispersed in a liquid. This Chapter introduces kinetic theory for thermal particles, for the computation of, among other things, their kinetic energies and the pressure they exert. The magnitude of thermal energy in comparison to chemical bond energies will also lead us into an aside on soft matter , the materials that are particularly susceptible to thermal energy at room temperature.
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Notes
- 1.
Also collisions between a particle and container walls are assumed to be purely elastic.
- 2.
See f.e. W. J. Moore, Physical Chemistry, Longman, London, fifth ed. (1972), pp. 148–150.
- 3.
The following derivation of ideal particle pressure is based on the treatment by James Clerk Maxwell (1831–1879) in his Theory of Heat (Longmans, London 1888); reprinted by Dover, Mineola, 2001.
- 4.
- 5.
\( < v_{\text{x}}^{2} > = - \left( {\frac{a}{\pi }} \right)^{1/2} \frac{d}{da}\int\limits_{ - \infty }^{ + \infty } {e^{{ - av_{\text{x}}^{2} }} } {\text{d}}v_{\text{x}} = - \left( {\frac{a}{\pi }} \right)^{1/2} \frac{d}{da}\left( {\frac{\pi }{a}} \right)^{1/2} = \frac{1}{2a} \)
- 6.
\( \int\limits_{0}^{\infty } {e^{{ - ax^{2} }} } x^{3} dx = - \frac{d}{da}\int\limits_{0}^{\infty } {e^{{ - ax^{2} }} x} dx\mathop = \limits^{{x^{2} = z}} - \frac{1}{2}\frac{d}{da}\int\limits_{0}^{\infty } {e^{ - az} } dz = - \frac{1}{2}\frac{d}{da}\left( {\frac{1}{a}} \right) = \frac{1}{{2a^{2} }} \)
- 7.
- 8.
Weak bonds between molecules resulting electrostatic attraction between a proton in one molecule and an electronegative atom in the other.
- 9.
Weak attractive force between electrically neutral molecules in close proximity caused by temporary attractions between electron-rich parts of one molecule and electron-poor parts of another.
- 10.
Written in 1918 by the Dutch poetess Henriette Roland Holst (1869–1952).
- 11.
My prose translation, see References for the original Dutch couplet.
References
The standard work on the development of kinetic theory: S.G. Brush, The kind of motion we call heat. A history of the kinetic theory of gases in the 19th century (Amsterdam, North-Holland, 1994).
For a more in-depth treatment of kinetic theory see: J. Jeans, An Introduction to the Kinetic Theory of Gases (Cambridge University Press, 1940).
For an enthusiastic introduction into the field of soft matter, read: R. Piazza, Soft Matter; the stuff that dreams are made of (Springer Netherlands, 2011).
A lucid textbook, not only on gases is D. Tabor, Gases, liquids and solids and other states of matter (Cambridge University Press, third ed. 1991).
The first couplet of Henriette Roland Holst’s poem in the Dutch original:
“De zachte krachten zullen zeker winnen
in’t eind – dit hoor ik als een innig fluisteren
in mij; zo’t zweeg zou alle licht verduistren
alle warmte zou verstarren van binnen”.
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Philipse, A.P. (2018). Kinetic Theory. In: Brownian Motion. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-98053-9_3
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