Z the number of electrons
3. For a system consisting of a mixture of particles behaving like an ideal gas and radiation, the total pressure and internal energy are given by:
P = (ρk_BT)/(μm_u) + (1/3)aT^4
u = (3/2)(ρk_BT)/(μm_u) + aT^4
Based on the discussed equations in class:
Γ(1) = ((dlnP)/(dlnρ))_s
(Γ(2))/(Γ(2)-1) = ((dlnP)/(dlnT))_s
Γ(3)-1 = ((dlnT)/(dlnρ))_s
Show we can obtain:
Γ(1) = (32-24β-3β^2)/(24-21β)
Γ(2) = (32-24β-3β^2)/(24-18β-3β^2)
Γ(3) = (32-27β)/(24-21β)
Where β = (P_g)/(P) is the ratio between gas pressure (from particles) and total pressure (including.