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## Homework Statement

A bottle with volume v containing 1 mole of argon is next to a bottle of volume v with 1 mole of xenon. both are connected with a pipe and tap and are same temp and pressure. the tap is opened and they are allowed to mix. What is the total entropy change of the system? Once the gases have fully mixed, the tap is shut and the gases are no longer free. what is the entropy change with this process?

## Homework Equations

ds= integral (nR/v) dv

## The Attempt at a Solution

imagining it as a reversible isotherm. I used

deltaS_mix = deltaS_1+deltaS_2

deltaS_1 = n_1*R*ln(V_1+V_2)/V_1

deltaS_2 = n_2*R*ln(V_1+V_2)/V_2

then adding them together and cancelling down from 2V/V etc i ended up with

R(ln2+ln2) = Rln4.

My Questions are:

Why does it ask for two separate entropy change calculations in the question?

In my textbook it uses xV and (x-1)V for the respective volumes and it ends up as

deltaS = -NK_b(x*lnx+(1-x)ln(1-x))

What does x represent here?

Thanks