Re: [Phys-l] Gibbs paradox

[Carl Mungan <mungan@usna.edu>]

> I THOUGHT the issue was this - rendered in comic form:
>
> In a  rectangular cardboard box, with a central removable partition,
> place a dozen ping pong balls each side of the partition.
>  Shake well.    1)
> Remove the partition. Shake well.      2)
> Replace the partition with equal numbers on each side again.    3)
>
> THEN
>
> In this cardboard box place the dozen balls in one side,
>  and place  the same quantity of ping pong balls dyed red
> in the other side of the central partition.    Shake Well.  4)
> Remove the partition. Shake well.      5)
> Replace the partition and rearrange the balls with equal numbers on each
> side again segregated by color.    6)
>
> The questions: are the entropy values of arrangement 1) , 2) and 3)
> significantly different?
> Are the entropy values of arrangement 4),  5)  and 6) significantly
> different?
> Are the two sets of  Ss for 1,2,3, and 4,5,6 significantly different? Is
> this paradoxical?
> Compare and contrast.    :-)

Thanks Brian, that's a helpful example, but to simplify it, calculate the entropy in just these two situations:

1. Put 100 ping-pong balls in a box with numbers written on them from 1 to 100. Shake. Calculate the entropy. This is the case of a monatomic ideal gas of "distinguishable but identical" atoms.

2. Repeat but this time don't put numbers on the balls. This is the case of a monatomic ideal gas of "indistinguishable" atoms.

Is there a factor of 100! in only one of your calculations and if so why? Does your answer depend on whether the lid of the box is transparent?