Perfect Gases and Ideal Mixtures

The relations which we have derived in the preceding section give a general framework for the equilibrium properties of thermodynamic system. The individual properties of particular systems have to be defined by so-called equations of state. 

An important class of systems is that of perfect gases with an equation of state given as 

Inserting (3.66) into (3.67) we directly obtain (9U/3V)j = 0 such that the 

If in a mixture of perfect gases with mole numbers N, N2,. .. each component behaves as if it were independent of the others, the equation of state of the component i is given as 

The validity of (3.76) actually goes far beyond mixtures of perfect gases. Systems in which the chemical potentials of the components can be expressed by (3.76) are called ideal systems. A special case of ideal systems are dilute solutions. A statistical derivation of (3.76) for dilute solutions may be found in LANDAU-LIFSHITZ, Theoretical Physics, Vol. V (1968). In dilute solutions, the mole fraction of a solute is approximately given as x. = N. /N where is the number of moles of the solvent. This enables us to rewrite the chemical potential of a solute approximately in terms of its concentration c. as 

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