Thermokinematic functions

Another feature of the present theory is that it provides a formalism for deducing a complete mathematical representation of a phenomenon. Such a representation consists, typically, of (1) Balance equations for extensive properties (such as the "equations of change" for mass, energy and entropy) (2) Thermokinematic functions of state (such as pv = RT, for simple perfect gases) (3) Thermokinetic functions of state (such as the Fourier heat conduction equation = -k(T,p)VT) and (4) The auxiliary conditions (i.e., boundary and/or initial conditions). The balances are pertinent to all problems covered by the theory, although their formulation may differ from one problem to another. Any set of... 

Equations 35 and 36 are called thermokinematic functions of state. (Note that the variable s was introduced along with Eq. 23 in order to facilitate elimination of and jr from Eqs. 19 and 20 respectively. A more natural way to eliminate these variables would be to simply multiply Eq. 19 by a, then subtract from Eq. 20. In the latter procedure entropy s would never be defined, rather a function for "internal availability" b(e,v) would arise. The choice of introducing s was made in order that the traditional results would be obtained.)... 

Next, the thermokinematic equations of change will be obtained. These are found by considering ideal relaxation processes, i.e., hypothetical ideal processes from any and every state visited during the real process to an arbitrary dead reference state. The foregoing equations of change are combined, for such a process, to eliminate all terms without parameter derivatives of properties thence, the existence of functions relating the properties (i.e., the "state principle") can be deduced. 

---