State space (thermodynamics)

In thermodynamics , a thermodynamic state space is a structure in a mathematical model for a thermodynamic system . The elements of a state space represent the macroscopic states of the considered thermodynamic system to be examined. These states are characterized by macroscopic features that must be ascertainable using methods from previous theories such as mechanics and electrodynamics. Examples of such characteristics are pressure, volume or magnetization. ${\displaystyle Z}$

State diagram for water

In thermostatics , mostly only the equilibrium states of simple thermodynamic systems are examined. In this case, the state space is often restricted to the set of equilibrium states of the system, here denoted by. For simple systems, an area of n-dimensional real space is then sufficient as a state space. For example, a two-dimensional area is used for the system of a certain amount of substance of a pure substance in a container . The point of this area corresponding to a state of equilibrium of the system can be identified as coordinates by the pressure on the container wall and the volume of the container, alternatively the temperature and volume or other suitable size pairs can be selected as coordinates. The choice of suitable coordinates for the points in the state space depends on the questions involved in a thermodynamic investigation. ${\displaystyle Z_{g}}$ ${\displaystyle \mathbb {R} ^{n}}$ ${\displaystyle \mathbb {R} ^{2}}$

A phase diagram is a projection of a state space for a simple system onto two coordinates. The connected areas of states of the same phase can be illustrated in it. The two-dimensional space of the equilibrium states of a pure substance is also often illustrated in a perspective 3-D drawing called a state diagram. The functional dependency of a state variable, such as pressure, is represented as a curved surface using two coordinates, such as volume and temperature. Different phases are then assigned to different regions of this area.

In the thermodynamics of irreversible processes , in which, for example, the heat transport in extended bodies is examined, the state space is usually an infinitely dimensional function space . In the case of heat transport, the temperature field is an element of this state space; the temperature is viewed as a function of location and time.

literature

• Klaus Stierstadt: Thermodynamics for the Bachelor degree . 2nd completely revised edition. Springer Verlag, Heidelberg 2018, ISBN 978-3-662-55715-0 , 9 Thermodynamics of Materials, p. 237–272 , doi : 10.1007 / 978-3-662-55716-7 (The chapter deals with the most important thermodynamic state functions and relationships between them. It gives examples of thermodynamic state spaces that model systems from a pure substance and illustrates them with state diagrams ).
• Günther Ludwig : Introduction to the basics of theoretical physics . tape 4 . Vieweg & Sohn, Braunschweig 1979, ISBN 3-528-09184-3 , XIV § 1.1 The state space, § 2.1 The problem of the state space, p. 8–11, 84–89 (Ludwig discusses the basic structures of a thermodynamic state space in thermostatics and shows the problem of expanding to non-equilibrium states and irreversible processes).

Individual evidence

1. ↑ Günther Ludwig : Introduction to the basics of theoretical physics . tape  4 . Vieweg & Sohn, Braunschweig 1979, ISBN 3-528-09184-3 , XIV Thermodynamics §1 Thermostatics, p. 8-84 .
2. ↑ en: Theodore Frankel : The Geometry of Physics - An Introduction . corrected and supplemented edition. Cambridge University Press, 2001, ISBN 0-521-38753-1 , 6.3 Heuristic Thermodynamics via Caratheodory, p.  178-187 .
3. ↑ Günther Ludwig : Introduction to the basics of theoretical physics . tape  4 . Vieweg & Sohn, Braunschweig 1979, ISBN 3-528-09184-3 , XIV Thermodynamics §2 Irreversible Processes, p. 85-145 .