Answer to Question #89301 in Molecular Physics | Thermodynamics for Shivam Nishad

Question

What is Gibb's paradox ? How is it resolved ?.

Answer 1

The Göbbs paradox is the absence of continuity for entropy when moving from mixing different gases to mixing identical gases: mixing entropy when moving from ideal gases with an arbitrarily small degree of difference to identical gases jumps from constant value to zero, which seems unexpected and illogical.

There is a mass of “solutions” to the paradox, for example, a solution that rejects its very existence is:

 the paradox reduces to a jump in the entropy behavior of the mixing ΔS with the continuous approach of certain parameters characterizing the mixed gases. If such a continuous convergence contradicts the laws of physics, that is, if the differences between gases can change only discretely, the Gibbs paradox disappears: it is not surprising that with a discrete change in the parameters of gases, the properties of their mixture also change discretely.