Thermodynamic functions for ideal gases

The equation of state for a mixture of ideal gases containing nu n2, n3. n . .. moles of each component or species is 

At constant temperature and mole numbers, Equation (4.25) becomes dG = V dP. On substitution of the ideal gas equation of state and integration, we obtain 

This equation is consistent with the concept that the Gibbs energy is a homogenous function of the first degree in the mole numbers. Comparison of this equation with Equation (7.49) together with the relation that Pt = Py( shows that 

Other thermodynamic functions can be derived from this equation. With 

2 The third law of thermodynamics, by which absolute values of the entropy can be determined, permits the calculation of the change of values of the Gibbs and Helmholtz energies with temperature. This subject is discussed in Chapter 15. 

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