I recently came across a text wherein it was described that for continuum assumption, one of the condition is thermodynamic equilibrium. For thermodynamic equilibrium, high frequency of inter molecular collision is required.
Can someone explain why high collision frequency implies thermodynamic equilibrium and not low collision frequencies?
Dear Andreas
Thanks for swift response. In lieu of your first question, I meant for gas and not liquid.
I would like to seek some further clarification. Say there are 10 molecules in a box. They will collide with each other after some time (or with some frequency). Their collision, to what I understand, transfer momentum energy from one molecule to other. Now say if this being done at very large pace (or frequency) how does it favor equilibrium?? Shouldn't it be vice versa as frequent collision means more agitation and less equilibrium.
Kindly correct me where I am wrong
Deewakar
@Deewakar: Maybe you textbook was a little unclear in its formulation. Usually you have thermodynamical equilibrium if you have a lot of particles because of the high collision frequency (assuming that you wait some time so that the system can reach TD equilibrium). - you need the high collisionality because TD equ. needs a random distribution of energy among your particles - if you have a neutral gas the energy can only be distributed via collisions. Imagine a cold gas in which you feed some hotter gas - the energy goes from the hotter to the colder gas through collisions (it has to be mentioned that you have also to look at rotational and vibrational degrees of freedom, not just onto the translational kinetic energy of your particles and also on the chemical potential). So, the more collisions you have the faster you reach your equilibrium.
@Andreas: you are right, the basic idea holds for liquids and gases, but the physical details differ in these two cases: in a gas you have longer mean free paths and the particles can move freely while in a liquid the average displacement will be much smaller. Furthermore you can have also no TD equ in gases even though they are also treatable as continuum (which goes in accordance with your post).
For a continuum description in terms of hydrodynamic equations, with heat conduction, diffusion and the like, it is usually required that there should be *local* thermal equilibrium. Complete thermodynamic equilibrium makes any kind of continuum description trivial, since one then has zero velocity and constant temperature, pressure and chemical potential.
But for a hydrodynamic description to hold, I do need to fulfil several conditions: I need to be able to define volume elements that are infinitesimal at the scale of the temperature or concentration variations I am interested in, but yet large enough to hold a number of particles large enough that the concept of thermodynamic equilibrium should be appropriate. And aditionally, I should have that these subsystems indeed do approach equilibrium on a time scale much shorter than the hydrodynamic time scales I am interested in. To that end I need enough collisions, since intermolecular collisions are in fact the means by which equilibrium is attained. In fact, what this means is that I should take my volume elements to be significantly larger than the mean free path. If that requirement conflicts with the requirement that the volume elements should be small with respect to the length over which temperatrure and concentration vary significantly, then a continuum appproach is impossible.
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