R2 1 r3

Unlike the exponent y in the case of perfect gas, the ri are not equal to the ratio Cp/Cv. The r depend on the equation of state. Figure 7.4 illustrates the variations of the r in the outer solar layers. The ri are equal to 5/3 for the neutral and fully ionized cases. In the domain of partial ionization (Fig. 7.2), the ri become lower than 4/3, which is destabilizing according to the Virial theorem (Sect. 1.3.2), however not catastrophic since the low ri occur only in a very small stellar mass fraction. Again, we may understand this behavior by noting, for example in the definition of r3 - 1, that the variation of T is reduced by partial ionization when the density and pressure increase. Figure 7.1 shows the corresponding variations of Vad =(r - 1)/r2.

Fig. 7.4 The adiabatic exponents ri as functions of temperature in the outer solar layers. In the neutral medium below 8000 K and in the fully ionized medium above T = 3 x 105 K,the various ri converge toward 5/3

7.4.2 Relation Between the ri and Specific Heats

Let us consider the internal energy by unit of mass U = U (T, q). One has dU = CydT + (dq . (7.59)

0 0