Onno Pols developed a systematic teaching account of stellar structure and stellar evolution. His 2011 notes connect hydrostatic equilibrium, energy transport and stellar thermodynamics, including the distinct adiabatic exponents needed when gas and radiation pressure both contribute.[ref]
Stellar Structure and Evolution by Onno Pols. Sections 3.3–3.4, especially the definitions of the adiabatic exponents
For example, a derivative describing how pressure responds to compression is not interchangeable with one describing the temperature response. Distinguishing them makes stability and energy-transport calculations usable beyond a single fixed-index ideal gas.
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