State function

A state variable is a macroscopic physical quantity, if necessary, together with other status variables describing the current state of a physical system, but is in principle variable. In contrast, the parameters describing the system, but will be assumed to be constant for the observed condition changes, referred to as parameters of the system. In an oscillatory system, for example, displacement and velocity can be state variables, mass and spring stiffness contrast parameter.

Two states are then considered to be different if the numerical values ​​are different at least one of the state variables. The switch between two different states is called a state change. Here, the state variables obey an equation of state.

State variables in thermodynamics

In thermodynamics, the clear description of the current state of a system is, among other things by means of the state variables:

• Pressure p
• ( absolute ) temperature T
• Volume V
• Particle number N or amount of substance n
• Density ρ
• Internal energy U
• Enthalpy H
• Entropy S
• Gibbs free energy, and Gibbs free energy, G

These state variables remain constant when a system is in thermodynamic equilibrium.

Some relationships between the different state variables have been grouped under the term of the Maxwell relations.

State variables are independent of the path, that is, they only describe the current state of a system and not, in what way it has come to this state.

In contrast, the process variables work and heat are path-dependent, ie they depend significantly on the shape of the state change.

Classification

Wherein the state variables are identified:

• Intensive state variables are the size of the system (of the amount of substance ) independently, eg Pressure and temperature.
• Extensive state variables are the size of the system -dependent ( of the amount of substance ), such as Volume and number of particles.

Beer Glass For example, the amount of beer in the glass is an extensive quantity, as two glasses contain twice the amount of beer. The temperature of the beer, however, is an intensive quantity, as two glasses of beer are not twice as warm as a single.

Another classification method divides the state variables in external and internal state variables.

Equations of state

Experimental findings indicate that these sizes can not be changed independently of each other, suggesting a certain number of degrees of freedom is also expressed in the Gibbs phase rule, or in determining the state of a system. The corresponding relationships between the state variables of a system describing equations of state. However, most real systems can not be described by equations of state, as between its state variables no mathematical relationship can be formulated.

Contrast, can be at very low density gases, such a correlation, under certain conditions, such as low pressure and high temperature, approximated by the assumption of an ideal behavior to describe what was formulated in the general gas equation:

With R = 8.3145 J / (mol · K) - universal gas constant

Also only an approximation, but also valid for more real gases, the van der Waals equation:

State functions and state variables

State functions such as the internal energy or the enthalpy of a system from the more basic state variables derived variables, which are called state variables.

This decides the individual case what size than state function and which is used as a state variable. Thus, e.g. the enthalpy H is used as a state variable, such as in the definition of G in the free energy:

State variables in astrophysics

In astrophysics state variables characterize, among other stars, for example, by their surface temperature, gravitational acceleration on the surface, luminosity, mass and radius are considered.

State variables in the system theory

Systems that can be described by ordinary differential equations ( of any order ), can always be described by an equivalent system of equations of first order differential equations. The independent variables of this equation system, which is referred to as a state equation or equation of state, the state variables and the state variables of the system. They span the state space. The state variables represent the state of the system. They are summarized in the state vector.

Variables which act from the outside of the system are referred to as input variables. Sizes which do not represent the condition, but can be observed are the output variables. Other variables which affect the system, but can be assumed as substantially constant, the parameters of the system, wherein a spring for example, the pendulum mass.