What is the entropy of mixing for a system of two monatomic ideal gases?

[Thadis]

I think I actually have solved it. I was right with the PV=nkT, I believe I previously messed up with the algebra.

Homework Statement

Using the same meathod as in the text, calculate the entropy of mixing for a system of two monatomic ideal gases, A and B, whose relative proportion is arbitrary. Let N be the total number of molecules and let x be the fraction of these that are species B. You should find that

ΔS=-Nk[xlnx+(1-x)ln(1-x)]

Check that this expression reduces to the one given in the text when x= 1/2.

Homework Equations

That S=Nk[ln(V(a/3n)^(3/2))+3/2] where a is just a whole bunch of stuff that I believe is irrelevant to the problem.

PV=nkT might be useful

also the fact that ln(x/y)=ln(x)-ln(y)

The Attempt at a Solution

I know that the change of entropy will just be S_final-S_original but I do not know what really changes between the final and the original situations. Do I have to use the Ideal Gas law find out how big the volume would be?

 

[Bystander]

This is a constant single pressure process; the original statement is about as obfuscated as is possible. "n" volumes of pure gases are mixed by volume fraction.