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The distinction between intensive and extensive properties has some theoretical uses. For example, in thermodynamics, the state of a simple compressible system is completely specified by two independent, intensive properties, along with one extensive property, such as mass. Other intensive properties are derived from those two intensive variables.
Extensive parameters are properties of the entire system, as contrasted with intensive parameters which can be defined at a single point, such as temperature and pressure. The extensive parameters (except entropy) are generally conserved in some way as long as the system is "insulated" to changes to that parameter from the outside. The truth of ...
where U is the internal energy (mass) of the system and N a refers to the extensive parameters of the system. Mathematically, the Ruppeiner geometry is one particular type of information geometry and it is similar to the Fisher–Rao metric used in mathematical statistics.
In thermodynamics, a physical property is any property that is measurable, and whose value describes a state of a physical system. Thermodynamic properties are defined as characteristic features of a system, capable of specifying the system's state.
The intensive (force) variable is the derivative of the (extensive) internal energy with respect to the extensive (displacement) variable, with all other extensive variables held constant. The theory of thermodynamic potentials is not complete until one considers the number of particles in a system as a variable on par with the other extensive ...
Given a set of extensive parameters X i (energy, mass, entropy, number of particles and so on) and thermodynamic forces F i (related to their related intrinsic parameters, such as temperature and pressure), the Onsager theorem states that [16]
The generalized force, X, corresponding to the external parameter x is defined such that is the work performed by the system if x is increased by an amount dx. E.g., if x is the volume, then X is the pressure. The generalized force for a system known to be in energy eigenstate is given by:
Yet also other variables may be used in that form. It is directly related to Gibbs phase rule, that is, the number of independent variables depends on the number of substances and phases in the system. An equation used to model this relationship is called an equation of state.