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?
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?