Entropy Change in an Isolated System

What is the correct expression for entropy change in the context of binary entropy of mixing?

a) ΔS = R * ln(Na/Nb)
b) ΔS = k * ln(Na/Nb)
c) ΔS = -R * ln(Na/Nb)
d) ΔS = -k * ln(Na/Nb)

Answer:

The correct expression for entropy change in the context of binary entropy of mixing is ΔS = -k * ln(Na/Nb), where 'k' is the Boltzmann constant and 'Na' and 'Nb' represent the number of microstates in each state.

Explanation: In the context of binary entropy of mixing in an isolated system initially separated by a partition, the proper expression for entropy change (ΔS) is given by the Boltzmann constant (k) and the natural logarithm of the ratio of the number of ways particles can be arranged in states A and B. Since entropy is understood as a measure of disorder or the number of microstates, when particles redistribute from an even distribution between two boxes to all ending up in one box, the change in entropy is positive.

The correct option for the entropy change in this scenario is d) ΔS = -k * ln(Na/Nb). Here, 'Na' and 'Nb' represent the number of microstates available in state 'a' and state 'b' respectively. The negative sign indicates a decrease in entropy when going from a more probable (or disordered) state to a less probable (or ordered) state, though in the context of the question, we are likely considering an increase in entropy as particles are typically moving to a more disordered state.