Gravity, Atmospheres, and Stellar Gases

An ideal-gas model without gravity treats a gas as spatially uniform under simple conditions. In a gravitational field, molecules have gravitational potential energy. Gas near the bottom of an atmosphere generally experiences greater pressure because it supports the weight of gas above it. Therefore: pressure generally decreases with altitude and gas density commonly decreases as well. For a small vertical change: **dp/dh = −ρg** The negative sign shows that pressure decreases as height increases. For an approximately isothermal ideal gas, combining hydrostatic balance with the ideal-gas equation leads qualitatively to an exponential decrease of pressure and density with height.

Gravity compresses stellar matter. High pressures, densities and temperatures inside stars mean that simple ideal-gas behaviour may require modification. This is one example of statistical mechanics extending beyond the simplest gas model.

**dp/dh = −ρg Ideal-gas relation: pV=NkT**