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Imagine a gas of N spherical particles that are free to distribute throughout either a large...

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Advance Math

Imagine a gas of N spherical particles that are free todistribute throughout either a large volume or a small one. Whydoes the gas spread out into a large volume? The tendency to spreadout is pressure and can be explained in terms of multiplicity orincreased probability. To illustrate this, let's create a simplermodel that we can visualize, solve exactly, and will illustrate theessence of the problem without the mathematical complexity. Foreach of the following, calculate the number of distinguishablearrangements of the vacancies and occupancies of the Nparticles in the M sites.

  1. Consider N=3 spherical particles spread out inM=5 equal size boxes that are arranged in a line. Theboxes are just big enough to hold at most one particle.

  2. Now consider N=3 spherical particles spread out in M=4boxes arranged in a line.

  3. Finally consider N=3 particles spread in onlyM=3 boxes.

  4. Based on these results why does a gas spread out into a largervolume?

Answer & Explanation Solved by verified expert
4.3 Ratings (744 Votes)
Case1 when N3 particles and M 5 boxes are present and each box is big enough to accomodate at most 1 particles    See Answer
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