Linked from
The 83 pages that link to Equation of state, each with the reason it gives.
Stellar coreRelated: It links core temperature and density to the pressure that supports the star.
Quark starRelated: A quark-matter equation of state predicts a star's mass, radius, and stability.
Classical fluidRelated: It closes fluid models by relating pressure to density and temperature.
Atmospheric physicsRelated: It links atmospheric temperature and pressure changes to air density.
High-energy-density plasmaRelated: It determines how the plasma responds when compressed or heated.