 Adiabatic exponents of a monatomic gas-radiation mixture

ID: adiabatic-exponents-of-a-monatomic-gas-radiation-mixture

For fixed-composition monatomic ideal gas plus equilibrium radiation pressure, specific internal energy is

u = 3 R T /2 + a_{r} T^{4} / ρ

d u = P d ρ / ρ^{2}

Γ_{3} - 1 = (8 - 6 β) / (24 - 21 β)

and

Γ_{2} = \frac{32 - 24 β - 3 β ^{2}}{24 - 18 β - 3 β ^{2}}, \nabla_{ad} = \frac{8 - 6 β}{32 - 24 β - 3 β ^{2}} .

The stellar gas-pressure fraction must be allowed to change along the adiabat. The pure-radiation and pure-gas limits give

Γ_{1} = Γ_{2} = 4/3

and

5/3

, respectively. Partial ionization or different gas heat capacities change these formulas.

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