2. A container is divided into two sides by a partition. Each side contains a different gas. The volume of

the entire container is V. The total number of moles of gas is n. The volume and number of moles of gas

on the right side is X₁V and zin while the volume and number of moles on the right side is z₂V and an.

Note x₁ and x2 are the component fractions. They satisfy X1+ X2= 1. The temperature and pressure

on both sides are equal. When the partition is removed, the gasses begin to mix until everywhere in

container is uniformly mixed.

(a) View the gas on the left side as undergoing an isothermal expansion from its initial volume to the

entire volume and view the gas on the right similarly to determine an expression for the total change

of entropy of the system, ∆S = ∆S₁+∆S2, in terms of n, R, 21, and 72.

(b) Compute the change of entropy for the case when nR = 5.0, ₁ = 0.20 and ₂ = 0.80.

(c) In the expression for ∆S found in part a let ₁ and 22-1-2. Differentiate the expression with

respect to a to determine the initial component fractions ₁ and ₂ for which the mixing process.

would result in the maximum increase in entropy.

(d) Compute the maximum possible change of entropy when -5.0.