Thermodynamic state

Last updated November 20, 2023

In thermodynamics, a thermodynamic state of a system is its condition at a specific time; that 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. Usually, by default, a thermodynamic state is taken to be one of thermodynamic equilibrium. This means that the state is not merely the condition of the system at a specific time, but that the condition is the same, unchanging, over an indefinitely long duration of time.

Properties that Define a Thermodynamic State

Temperature (T) represents the average kinetic energy of the particles in a system. It's a measure of how hot or cold a system is.
Pressure (P) is the force exerted by the particles of a system on a unit area of the container walls.
Volume (V) refers to the space occupied by the system.
Composition defines the amount of each component present for systems with more than one component (e.g., mixtures).

Thermodynamic Path

When a system undergoes a change from one state to another, it is said to traverse a path. The path can be described by how the properties change, like isothermal (constant temperature) or isobaric (constant pressure) paths.

Thermodynamics sets up an idealized conceptual structure that can be summarized by a formal scheme of definitions and postulates. Thermodynamic states are amongst the fundamental or primitive objects or notions of the scheme, for which their existence is primary and definitive, rather than being derived or constructed from other concepts.^[1]^[2]^[3]

A thermodynamic system is not simply a physical system.^[4] Rather, in general, infinitely many different alternative physical systems comprise a given thermodynamic system, because in general a physical system has vastly many more microscopic 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. The number is always 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. The choice is usually made on the basis of the walls and surroundings that are relevant for the thermodynamic processes that are to be considered for the system. For example, if it is intended to consider heat transfer for the system, then a wall of the system should be permeable to heat, and that wall should connect the system to a body, in the surroundings, that has a definite time-invariant temperature.^[5]^[6]

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.^[7] 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.^[8]

State variables and state functions

A thermodynamic system can be identified or described in various ways. Most directly, it can be identified by a suitable set of state variables. Less directly, it can be described by a suitable set of quantities that includes state variables and state functions.

The primary or original identification of the thermodynamic state of a body of matter is by directly measurable ordinary physical quantities. For some simple purposes, for a given body of given chemical constitution, a sufficient set of such quantities is 'volume and pressure'.

Besides the directly measurable ordinary physical 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. There are many such state functions. Examples are internal energy, enthalpy, Helmholtz free energy, Gibbs free energy, thermodynamic temperature, and entropy. For a given body, of a given chemical constitution, when its thermodynamic state has been fully defined by its pressure and volume, then its temperature is uniquely determined. Thermodynamic temperature is a specifically thermodynamic concept, while the original directly measureable state variables are defined by ordinary physical measurements, without reference to thermodynamic concepts; for this reason, it is helpful to regard thermodynamic temperature as a state function.

A passage from a given initial thermodynamic state to a given final thermodynamic state of a thermodynamic system is known as a thermodynamic process; usually this is transfer 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 or quasi-static 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 three variables out of the following four: amount of substance, pressure, temperature, and volume. Thus, the thermodynamic state would range over a three-dimensional state space. The remaining variable, as well as other quantities such as the internal energy and the entropy, would be expressed as state functions of these three variables. The state functions satisfy certain universal constraints, expressed in the laws of thermodynamics, and they depend on the peculiarities of the materials that compose the concrete system.

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

Equilibrium state

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.

Related Research Articles

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

Entropy is a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter. Another statement is: "Not all heat can be converted into work in a cyclic process."

The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes in which two principal forms of energy transfer, heat and thermodynamic work, are distinguished that modify a thermodynamic system of a constant amount of matter. The law also defines the internal energy of a system, an extensive property for taking account of the balance of these energies in the system. Energy cannot be created or destroyed, but it can be transformed from one form to another. In an isolated system the sum of all forms of energy is constant.

The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowler in the 1930s, long after the first, second, and third laws had been widely recognized.

Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium, there are no net macroscopic flows of matter nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs.

The internal energy of a thermodynamic system is the energy contained within it, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. It includes the thermal energy, i.e., the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. The internal energy of an isolated system cannot change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics.

A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics. A thermodynamic system may be an isolated system, a closed system, or an open system. An isolated system does not exchange matter or energy with its surroundings. A closed system may exchange heat, experience forces, and exert forces, but does not exchange matter. An open system can interact with its surroundings by exchanging both matter and energy.

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions.

The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various parameters for thermodynamic processes, such as thermodynamic work and heat, and establish relationships between them. They state empirical facts that form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general and are applicable in other natural sciences.

Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.

Equilibrium Thermodynamics is the systematic study of transformations of matter and energy in systems in terms of a concept called thermodynamic equilibrium. The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as the system settles into its final equilibrium state, work is extracted.

In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy, pressure and volume, or chemical potential and particle number. In fact, all thermodynamic potentials are expressed in terms of conjugate pairs. The product of two quantities that are conjugate has units of energy or sometimes power.

Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes.

Thermodynamic work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. This exchange results in externally measurable macroscopic forces on the system's surroundings, which can cause mechanical work, to lift a weight, for example, or cause changes in electromagnetic, or gravitational variables. The surroundings also can perform work on a thermodynamic system, which is measured by an opposite sign convention.

The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microstates that constitute thermodynamic systems.

In thermodynamics, heat is the thermal energy transferred between systems due to a temperature difference. In colloquial use, heat sometimes refers to thermal energy itself. Thermal energy is the kinetic energy of vibrating and colliding atoms in a substance.

<span class="mw-page-title-main">Temperature</span> Physical quantity of hot and cold

Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the kinetic energy of the vibrating and colliding atoms making up a substance.

A thermodynamic operation is an externally imposed manipulation that affects a thermodynamic system. The change can be either in the connection or wall between a thermodynamic system and its surroundings, or in the value of some variable in the surroundings that is in contact with a wall of the system that allows transfer of the extensive quantity belonging that variable. It is assumed in thermodynamics that the operation is conducted in ignorance of any pertinent microscopic information.

References

↑ Callen, H.B. (1960/1985), p. 13.
↑ Carathéodory, C. (1909).
↑ Marsland, R. $III$ , Brown, H.R., Valente, G. (2015).
↑ Jaynes, E.T. (1965), p. 397.
↑ Prigogine, I., Defay, R. (1950/1954), p. 1.
↑ Zemanksy, M.W., Dittman, R.H. (1937/1981), p. 6.
↑ Planck, M., (1923/1927), p. 3.
↑ Eu, B.C. (2002).

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