Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
••• Entropy of Mixing. Consider a box containing N particles. A partition separates the right and left halves of the box and there are N/2 particles to the right of the partition and N/2 particles to the left. Suddenly, the partition breaks allowing the particles on the right and left to freely mix. If the particles are indistinguishable, the change in entropy of the system when the partition breaks is negligible. However, if the particles are distinguishable (for instance, if the right and left halves contain different isotopes of the same inert gas) then there is an increase in entropy, called the entropy of mixing, equal to ∆S = kN ln 2. Prove these statements.
In the nineteenth century, before the development of quantum mechanics and the notion of indistinguishability, physicists thought that identical particles were distinguishable and that there should therefore be an increase in entropy when identical gases mix. Experimentally, no such increase was observed and this puzzling state of affairs was called Gibb’s paradox.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.