Sunday, 8 January 2017

thermodynamics - How can there be any probability of finding the molecules clustered in half of the box,the other being empty?



Suppose,there are six molecules(indistinguishable) constantly jostling around in a box. The central configuration is when there are $3$ molecules in either halves of the box and having probability $31.3$%. However,



it is surprising that there is probability,however small, of finding all the molecules in the corner half of the box. - Resnick,Halliday,Walker.



Doesn't it break the Second law of thermodynamics? The configuration where the molecules are confined in a corner isn't possible. But math is showing otherwise. They have probability $1.6$%. How can it be possible??


[Even Planck also hesitated and at first rejected the underlying assumption of Boltzmann's approach which allows the Second law to be violated momentarily during $\text{fluctuations}^1$.


$1$"A small probability exists that all the molecules of a system of confined gas might appear for an instant in just one corner of the container. This is called energy fluctuation."- Boltzmann]




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