Two quite different Saha equations modified to a two-temperature plasma were proposed and employed in many literatures.In order to clear up this confusion phenomenon lasted for a few decades in the community of thermal plasma science and technology,this paper re-examines the thermodynamic derivation of the two-temperature Saha equations.It is pointed out that the modified Saha equation deduced by using the minimum Gibbs or Helmholtz free energy is incorrect for the two-temperature plasma.Instead,a more rigorous derivation is presented here from the basic thermodynamic principle that the entropy in an isolated system always assumes its maximum value at chemical equilibrium.
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