- #1

Ionophore

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I'm working through Callen to try and teach myself some thermodynamics before the semester starts and I have to take pchem. I'm pretty stumped on problem 4.2-4.

## Homework Statement

A system obeys the eqns:

T=A(v^2)/s

P=-2Avln(s)

(A is some positive constant)

The system undergoes free expansion from v_0 to v_f. Find the final temperature in terms of t_initial, v_0 and v_f. Find also the increase in molar entropy.

## The Attempt at a Solution

I've fumbled around a bit. I found the "fundamental relation" by integrating (by inspection) du=Tds - Pdv, it's:

U=A(v^2)ln(s)

But this leads me nowhere.

The only other thing I can see to do is say that in a "free expansion," du=0, and therefore Tds = Pdv. I can substitute into this the equations for T and P given in the problem and integrate. I end up with something ugly and it's not clear to me where to go from there. Integration gives:

(1/2)ln(s)^2 = 2ln(v)

Any help appreciated,

-Ben