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

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Homework Help Overview

The problem involves calculating the height of a mountain based on the boiling points of a liquid at different elevations and its latent heat. The context is rooted in statistical mechanics, specifically relating to the Clausius-Clapeyron Equation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the canonical partition function to derive pressure as a function of height and apply it within the Clausius-Clapeyron Equation. Some participants question the necessity of the mass of the liquid molecule, which is not provided.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and the implications of missing information. There is an acknowledgment of the challenges faced in applying the Clausius-Clapeyron Equation due to the lack of specific parameters.

Contextual Notes

Participants note that the mass of the liquid molecule is not given, which may impact the application of the Clausius-Clapeyron Equation. The problem is framed within the constraints of a homework assignment, which may limit the information available for solving it.

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.
 
Last edited:
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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
 

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