Maxwell Boltzmann Distribution: Hard sphere; remember a hard sphere is a classical analogy of a rigid sphere whose surfaces do not deform when an external object comes into contact. This essentially means the incoming object is scattered elastically that is without loss of kinetic energy, only momenta magnitude and directions are changed in accordance with the conservation of linear momentum. Photo Credit: mdashf.org

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Maxwell Boltzmann distribution for a classical ideal gas

i. We assume a dilute gas which is enclosed by a thermally insulated container on all sides.

Dilute gas in a thermally insulated container: Dilute means concentration of gas molecules is low. Insulated implies there is no reasonable flow of heat energy across the walls of the container.

ii. Each molecule is assumed to be a hard sphere which moves randomly in all directions such that its velocity vary from – infinity to + infinity.

Hard sphere: Remember a hard sphere is a classical analogy of a rigid sphere whose surfaces do not deform when an external object comes into contact. This essentially means the incoming object is scattered elastically that is without loss of kinetic energy, only momenta magnitude and directions are changed in accordance with the conservation of linear momentum.

iii. When molecules collide they do not lose energy or time. They bounce off each other so that ‘energy’ and ‘momenta’ are conserved.

We would like to obtain an expression for velocity distribution function. That is we would like to know the fraction of molecules having velocity between v to v+dv for all possible values of velocity.

For this we assume an ensemble of molecules in equilibrium. The ratio of number of molecules in a velocity range to the total number of molecules N gives the probability of finding a molecule in that velocity range.

v. The “phase space” of the ensemble of molecules is defined by a 6 N dimensional space, which constitutes of 3 N spatial components and 3 N velocity components of the N molecules in equilibrium. For a more advanced concept of phase space check the following statistical mechanics lecture.

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Telos is Greek for end. So nice.

Sean has this lucidly written this article on our existential moorings .. “Why we move towards Future differently from Past eg is Thermodynamics and Arrow of Time”. What I picked up is though, two interesting cognates of Greek with Sanskrit. Telos is Greek for End. Well it is so for Sanskrit, (hence ILS, almost all Indian Language System you can bet); See t is almost always tied to s, eg store, starvation. Its one syllable unit. (transliteration locked or locked by alphabet occurrence, origin) So you can add the s. (phonetic also means you can eg say selos, telos etc) stelos. l is a y or j etc, a softer rendering which makes the l not so perceptible any more. Actually l/j alternation is very prominent (as are m/b and p/e etc) so seyas (or any closer phonetics) Thats nothing but Indi: shesh = end. Also its worthwhile to mention that the Odia: sari (sariba, sarijiba) originates here, because l/r

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