Question

The lattice model for mixture (diffusion). There are S cells to be occupied randomly by two types of particles (A or B). Fac accommodate only one particle, either A or B. The total number of particles (N) is also 8 (N- NA + NB-4 + 4 = 8). The 8 cells are separated into 4 left (L) and 4 right (R) ones. A macrostate can be characterized by giving the number of A and B type particles in each compartment. For example: L(3A. IB), which implies R(IA,3B). The total number of microstates (the multiplicity of a macrostate) is Ω-Ω1nR , that is to each L-microstate there can be more than one R- microstates. For example the L(3A.1 B) / R(IA.3B) macrostate has microstates of (AAAB), (BBBA) ABAA) (BBAB), and so on. Evaluate the possible microstates for each macrostate and identify the macrostate with the highest multiplicity? What is the entropy (S k InQ) for that macrostate? Does the result suggest even L R mixing?

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Answer 1

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