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the state spontaneously reached by a thermodynamic system after a sufficiently long time when isolated from its surroundings; the parameters of state of the system then no longer vary with time. Isolation does not preclude the possibility of contacts of a certain type with the surroundings, such as thermal contact with a thermostat or the exchange of matter. The process by which the system reaches equilibrium is called relaxation. When the system is in thermodynamic equilibrium, all irreversible processes associated with energy dissipation—including thermal conduction, diffusion, and chemical reactions—come to a halt. The equilibrium state of the system is determined by the values of its external thermodynamic parameters, such as volume and electric or magnetic field strength, and by the value of the temperature. Strictly speaking, the parameters of state of a system in a state of equilibrium are not absolutely fixed, since in very small volumes they can experience small fluctuations about their average values. The isolation of a system is generally achieved by using stationary walls impermeable to matter. If, as in Dewar flasks, the stationary walls isolating the system are essentially non-heat-conducting—that is, if adiabatic walls are used—the energy of the system remains constant. When heat-conducting, or diathermal, walls are used between the system and the surroundings, heat exchange is possible until equilibrium is established. When such a system is in prolonged thermal contact with an environment having a very high heat capacity, the temperatures of the two systems are equalized, and thermodynamic equilibrium is reached. When the walls are semipermeable to matter, thermodynamic equilibrium is reached if the chemical potentials of the environment and the system are equalized through the exchange of matter between the system and the environment.
One of the conditions for thermodynamic equilibrium is mechanical equilibrium. In mechanical equilibrium, all macroscopic motions of parts of the system are impossible, but translational motion and rotation of the system as a whole are permissible. In the absence of external fields and rotation of the system, constant pressure throughout the entire system is a condition for mechanical equilibrium. Other necessary conditions for thermodynamic equilibrium are constant temperature and constant chemical potential throughout the system. The sufficient conditions for thermodynamic equilibrium (stability conditions) can be obtained from the second law of thermodynamics (the principle of maximum entropy). Examples of these conditions are an increase in pressure as the volume decreases at constant temperature and a positive value of the heat capacity at constant pressure. In the general case, a system is in thermodynamic equilibrium when a minimum value is had by the thermodynamic potential that corresponds to the variables that are independent under the conditions of the experiment. For example, if the volume and temperature are constant, the Helmholtz free energy must have a minimum value; if the pressure and temperature are constant, the Gibbs free energy must have a minimum value.
REFERENCESKubo, R. Termodinamika. Moscow, 1970. (Translated from English.)
Samoilovich, A. G. Termodinamika i statisticheskaia fizika, 2nd ed. Moscow, 1955.
Waals, J. D. van der, and F. Konstamm. Kurs termostatiki, part 1: Obshchaia termostatika. Moscow, 1936. (Translated from English.)
D. N. ZUBAREV