Thermodynamic state

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For thermodynamics, a thermodynamic state of a system is fully identified by values of a suitable set of parameters known as state variables, state parameters or thermodynamic variables. Once such a set of values of thermodynamic variables has been specified for a system, the values of all thermodynamic properties of the system are uniquely determined.

Thermodynamics sets up an idealized formalism that can be summarized by a system of postulates of thermodynamics. Thermodynamic states are amongst the fundamental or primitive objects or notions of the formalism, in which their existence is formally postulated, rather than being derived or constructed from other concepts.[1][2]

A thermodynamic system is not simply a physical system.[3] Rather, in general, indefinitely many different alternative physical systems comprise a given thermodynamic system, because in general a physical system has vastly many more detailed characteristics than are mentioned in a thermodynamic description. A thermodynamic system is a macroscopic object, the microscopic details of which are not explicitly considered in its thermodynamic description. The number of state variables required to specify the thermodynamic state depends on the system, and is not always known in advance of experiment; it is usually found from experimental evidence. Always the number is two or more; usually it is not more than some dozen. Though the number of state variables is fixed by experiment, there remains choice of which of them to use for a particular convenient description; a given thermodynamic system may be alternatively identified by several different choices of the set of state variables.[4][5]

For equilibrium thermodynamics, in a thermodynamic state of a system, its contents are in internal thermodynamic equilibrium, with zero flows of all quantities, both internal and between system and surroundings. For Planck, the primary characteristic of a thermodynamic state of a system that consists of a single phase, in the absence of an externally imposed force field, is spatial homogeneity.[6] For non-equilibrium thermodynamics, a suitable set of identifying state variables includes some macroscopic variables, for example a non-zero spatial gradient of temperature, that indicate departure from thermodynamic equilibrium. Such non-equilibrium identifying state variables indicate that some non-zero flow may be occurring within the system or between system and surroundings.[7]

State functions[edit]

Main article: State function

Besides the thermodynamic variables that originally identify a thermodynamic state of a system, the system is characterized by further quantities called state functions, which are also called state variables, thermodynamic variables, state quantities, or functions of state. They are uniquely determined by the thermodynamic state as it has been identified by the original state variables. A passage from a given initial thermodynamic state to a given final thermodynamic state of a thermodynamic system is known as a thermodynamic process; it typically involve transfers of matter or energy between system and surroundings. In any thermodynamic process, whatever may be the intermediate conditions during the passage, the total respective change in the value of each thermodynamic state variable depends only on the initial and final states. For an idealized continuous process, this means that infinitesimal incremental changes in such variables are exact differentials. Together, the incremental changes throughout the process, and the initial and final states, fully determine the idealized process.

In the most commonly cited simple example, an ideal gas, the thermodynamic variables would be any two variables out of the following four: entropy, pressure, temperature, and volume. Thus the thermodynamic state would range over a two-dimensional state space. The remaining two variables, as well as other quantities such as the internal energy, would be expressed as state functions of these two variables. The state functions satisfy certain universal constraints, but ultimately they depend on the materials involved in the concrete system.

Various thermodynamic diagrams have been developed to model the transitions between thermodynamic states.

Equilibrium state[edit]

Physical systems found in nature are practically always dynamic and complex, but in many cases, macroscopic physical systems are amenable to description based on proximity to ideal conditions. One such ideal condition is that of a stable equilibrium state. Such a state is a primitive object of classical or equilibrium thermodynamics, in which it is called a thermodynamic state. Based on many observations, thermodynamics postulates that all systems that are isolated from the external environment will evolve so as to approach unique stable equilibrium states. There are a number of different types of equilibrium, corresponding to different physical variables, and a system reaches thermodynamic equilibrium when the conditions of all the relevant types of equilibrium are simultaneously satisfied. A few different types of equilibrium are listed below.

  • Thermal Equilibrium: When the temperature throughout a system is uniform, the system is in thermal equilibrium.
  • Mechanical Equilibrium: If at every point within a given system there is no change in pressure with time, and there is no movement of material, the system is in mechanical equilibrium.
  • Phase Equilibrium: This occurs when the mass for each individual phase reaches a value that does not change with time.
  • Chemical Equilibrium: In chemical equilibrium, the chemical composition of a system has settled and does not change with time.


  1. ^ Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8, p. 13.
  2. ^ Carathéodory, C. (1909).
  3. ^ Jaynes, E.T. (1965), p. 397.
  4. ^ Prigogine, I., Defay, R. (1950/1954), p. 1.
  5. ^ Zemanksy, M.W., Dittman, R.H. (1937/1981), p. 6.
  6. ^ Planck, M., (1923/1927), p. 3.
  7. ^ Eu, B.C. (2002).


  • Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3.
  • Cengel, Yunus; Michael A. Boels (2011). Thermodynamics An Engineering Approach. New York, NY: McGraw-Hill. ISBN 978-0-07-352932-5. 
  • Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8.
  • Carathéodory, C. (1909). "Untersuchungen über die Grundlagen der Thermodynamik". Mathematische Annalen 67: 355–386. doi:10.1007/BF01450409.  A translation may be found here. A mostly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA.
  • Eu, B.C. (2002). Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics, Kluwer Academic Publishers, Dordrecht, ISBN 1-4020-0788-4.
  • Jaynes, E.T. (1965). Gibbs vs. Boltzmann entropies, Am. J. Phys., 33: 391–398.
  • Modell, Michael; Robert C. Reid (1974). Thermodynamics and Its Applications. Englewood Cliffs, NJ: Prentice-Hall. ISBN 0-13-914861-2. 
  • Planck, M., (1923/1927). Treatise on Thermodynamics, translated by A. Ogg, third English edition, Longmans, Green and Co., London.
  • Prigogine, I., Defay, R. (1950/1954). Chemical Thermodynamics, Longmans, Green & Co, London.
  • Tisza, L. (1966). Generalized Thermodynamics, M.I.T. Press, Cambridge MA.
  • Zemanksy, M.W., Dittman, R.H. (1937/1981). Heat and Thermodynamics. An Intermediate Textbook, sixth edition, McGraw-Hill Book Company, New York, ISNM 0-07-072808-9.

See also[edit]