The polytropic (adiabatic) index for pure hydrogen plasma is analytically calculated as function of reciprocal temperature and degree of ionization. Additionally, the polytropic index is graphically represented as a function of temperature and density. It is concluded that the partially ionized hydrogen plasma cannot be exactly polytropic. The calculated deviations from the mono-atomic value 5/3 are measurable. The analytical result for pure hydrogen plasma is a test example how this approach can be extended for arbitrary gas cocktail.
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