The Model System with Potential Energy

Until now, we have assumed that the particles in our model gas have no forces acting on them except those due to collisions with the container. We now modify our model to include additional forces on the particles. 

A one-body force is independent of the locations of other particles. Electrostatic forces on a charged particle due to an external electric field are one-body forces. Near the surface of the earth the force of gravity on a particle is also a one-body force. This gravitational force on an object corresponds to a potential energy 

We now assert without proof that the Boltzmann probability distribution holds for this total energy  

Assume that the earth s atmosphere has a constant temperature of 298 K (not an accurate assumption). Estimate the pressure at 8900 m above sea level (roughly the altitude of Mount Everest). Assume that air is a single ideal gas with a molar mass of 0.029 kg mol T 

Representing the high-altitude state as 2 and the sea-level state as 1, the probabihty ratio is 

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Section 9.7 The Model System with Potential Energy... 

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