| Abstrakt: |
In equilibrium thermodynamics systems can be described in terms of properties which are either (1) intensive, (2) extensive, or (3) neither intensive nor extensive. While they can vary with spatial location in nonequilibrium systems, intensive properties are homogenous functions of degree (or order) zero (k = 0) and can be measured at any point. Temperature must always be intensive, as required by the laws of thermodynamics. This fundamental aspect of temperature is preserved whether dealing with equilibrium or nonequilibrium systems, as the latter can be analyzed with local thermal equilibrium or reduced time intervals. As for extensive properties, given equilibrium, they are homogeneous functions of degree one (k = 1) and consequently, are both additive and dependent on spatial extent. Conversely, properties which are neither intensive nor extensive represent homogeneous functions of specific degree ( 0 < k < 1 ) which, while nonadditive, remain dependent on some aspect of spatial extent. Importantly, the determination of whether some properties (e.g., length and surface area) are extensive or neither intensive nor extensive remains system dependent. Since thermodynamic properties are homogenous functions, all thermodynamic expressions must be balanced. This requirement extends beyond simple dimensionality. The intensive or extensive character of any given thermodynamic expression must be preserved on either side. In this regard, the existence of properties which are neither intensive nor extensive provides significant insight into the validity of thermodynamic expressions. The inclusion of such properties within expressions can only be allowed when their presence results in thermodynamic balance. Otherwise, the resulting expressions violate the laws of thermodynamics. This is often manifested in temperature relations which are nonintensive. |
