The integration constant, gk T

In the preceding work it was not necessary to consider the dependence of the integration constant on the temperature and in many cases it is not necessary to do so. At a given temperature it is a constant and, as long as only differences in the thermodynamic functions are considered at the same temperature, this constant cancels. 

It is informative, however, to consider the dependence of this function on the temperature. Since we know it is characteristic of the pure gas, we consider only 1 mole of a pure gas. Moreover, we limit the discussion to an ideal gas. There are two possible methods, one concerning the energy and entropy and the other the enthalpy and entropy, but we use only the energy and entropy here. The differential of the energy of 1 mole of ideal gas is dE = v dT. On 

Although the heat capacity is determinable, e and s are not known, and hence the value of g(T) is not known. When we consider the difference, g(T2)— 0( 1 ) the integrals involving the heat capacities can be evaluated, but the term (7 2 — TJs still remains. As long as s is unknown, this term cannot be evaluated. The evaluation of S is the province of the third law of thermodynamics. 

The thermodynamic equations for the Gibbs energy, enthalpy, entropy, and chemical potential of pure liquids and solids, and for liquid and solid solutions, are developed in this chapter. The methods used and the equations developed are identical for both pure liquids and solids, and for liquid and solid solutions therefore, no distinction between these two states of aggregation is made. The basic concepts are the same as those for gases, but somewhat different methods are used between no single or common equation of state that is applicable to most liquids and solids has so far been developed. The thermodynamic relations for both single-component and multicomponent systems are developed. 

The thermodynamic functions have been defined in terms of the energy and the entropy. These, in turn, have been defined in terms of differential quantities. The absolute values of these functions for systems in given states are not known.1 However, differences in the values of the thermodynamic functions between two states of a system can be determined. We therefore may choose a certain state of a system as a standard state and consider the differences of the thermodynamic functions between any state of a system and the chosen standard state of the system. The choice of the standard state is arbitrary, and any state, physically realizable or not, may be chosen. The nature of the thermodynamic problem, experience, and convention dictate the choice. For gases the choice of standard state, defined in Chapter 7, is simple because equations of state are available and because, for mixtures, gases are generally miscible with each other. The question is more difficult for liquids and solids because, in addition to the lack of a common equation of state, limited ranges of solubility exist in many systems. The independent variables to which values must be assigned to fix the values of all of the 

---