Latent heat, liquid-gas transition, stat mech with gravity

mchan1014
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Problem solved.

Homework Statement


The boiling point of a certain liquid is 95OC at the top of a mountain
and 105OC at the bottom. Its latent heat is 1000 cal/mole. Calculate the
height of mountain.
It's Q4 of chapter 15 in Statistical Mechanics by S.K. Ma

Homework Equations


it should be the Clausius-Clapeyron Equation

The Attempt at a Solution


I tried to use the canonical partition function to derive the pressure in terms of height, and then plug it into the Clausius-Clapeyron Equation, but it is not successful.
 
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as the pressure at height z is P(z) = P(0) exp ( - mgz / kT )
I plug it into the Clausius-Clapeyron Equation and found that it depends on m, the mass of the liquid molecule, which is not given
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.

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