F Thermodynamic Approach State Variables

1 The method of local state postulates that the thermodynamic state of a continuum at a given point and instant is completely defined by several state variables (also known as thermodynamic or independent variables). A change in time of those state variables constitutes a thermodynamic process. Usually state variables are not all independent, and functional relationships exist among them through equations of state. Any state variable which may be expressed as a single valued function of a set of other state variables is known as a state function.

2 The time derivatives of these variables are not involved in the definition of the state, this postulate implies that any evolution can be considered as a succession of equilibrium states (therefore ultra rapid phenomena are excluded).

3 The thermodynamic state is specified by n + 1 variables v\,v2, ••• ,vn and s where vi are the thermodynamic substate variables and s the specific entropy. The former have mechanical (or electromagnetic) dimensions, but are otherwise left arbitrary in the general formulation. In ideal elasticity we have nine substate variables the components of the strain or deformation tensors.

4 The basic assumption of thermodynamics is that in addition to the n substate variables, just one additional dimensionally independent scalar paramer suffices to determine the specific internal energy u. This assumes that there exists a caloric equation of state u = u(s, v, X)

5 In general the internal energy u can not be experimentally measured but rather its derivative.

For instance we can define the thermodynamic temperature 0 and the thermodynamic "ten-

where the subscript outside the parenthesis indicates that the variables are held constant.

7 By extension Ai = —pri would be the thermodynamic "force" and its dimension depends on the one of vi.

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