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Show THERMODYNAMIC QUANTITIES OF PERFECT IV. GAS SYSTEMS The Perfect Boltzmann Gas A. We shall consider in the present and subsequent sectiops composed of independent indistinguishable. for the atoms and molecules system will be gi,ven as H = (11-23) we see that H for the Ha + + • • (IV-I) • Hamiltonian function for each Ha' RbI etc., are the where are independent contributions, of sum a which gas the classical Hamiltonian function Suppose H is Then from Equation system. (particles), a particle. Similarly, then for the Hamiltonian operator (rV-2) Let the eigenvalues and eigenfunctions of by €a! €b' • • • and H,II' 'I' Va' *b' = = = Thus the possible respectively. · · · (Ra + H_ -0 + (€a + €b + Ha' Hb' • • etc., be denoted Then .) ,:Ir'l'a, ,J'b '1" .) (IV-3) V (Iv-4) Eljr energy eigenvalues for the whole system are of the form which is just the sm of the separate it the Hamiltonian operator for the energy for that particle, particles in the one and - 26 particle sum system. - energies, over is all €a' €b' given, • we Thus, may determine indistinguishable |
