It is important that plasma composition is calculated in a manner consistent with statistical mechanics, particularly since the Boltzmann equation is the basis from which transport coefficients and the fluiddynamic equations are derived. It is shown from statistical mechanical considerations based on the Boltzmann equation and the Htheorem that it is (i) not possible for a plasma to have more than one temperature in equilibrium in the absence of external forces and gradients, and (ii) not possible to draw conclusions about the change in entropy of a plasma in the presence of external forces and gradients. Derivations of the twotemperature Saha equation, and more generally calculations of the composition of a multitemperature plasma, that are based on entropy maximization are therefore invalid. A thermodynamic derivation of the composition of a multitemperature plasma that is consistent with the statistical mechanical results is presented. The derivation shows that the equilibrium composition of a plasma can be correctly calculated by minimization of the internal or free energy.