Entropy of mixing. Suppose that a system of N atoms of type A is placed in diffusive contact with a system of N atoms of type B at the same temperature and volume. Show that after diffusive equilibrium is reached the total entropy is increased by 2Nlog2. The entropy increase 2Nlog2 is known as the entropy of mixing. If the atoms are identical (A≡B), show that there is no increase in entropy when diffusive contact is established. The difference in the results has been called the Gibbs paradox.