In thermodynamics, a quantity that is well defined so as to describe the path of a process through the

equilibrium state 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 thermod ...

space of a

thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...

is termed a process function, or, alternatively, a process quantity, or a path function. As an example,

mechanical work In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...

and

heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...

are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system. Path functions depend on the path taken to reach one state from another. Different routes give different quantities. Examples of path functions include

work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal t ...

and

arc length ARC may refer to: Business * Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s * Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services * ...

. In contrast to path functions, state functions are independent of the path taken. Thermodynamic

state variables A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...

are point functions, differing from path functions. For a given state, considered as a point, there is a definite value for each state variable and state function. Infinitesimal changes in a process function are often indicated by to distinguish them from infinitesimal changes in a state function which is written . The quantity is an

exact differential In multivariate calculus, a differential or differential form is said to be exact or perfect (''exact differential''), as contrasted with an inexact differential, if it is equal to the general differential dQ for some differentiable function ...

, while is not, it is an

inexact differential An inexact differential or imperfect differential is a differential whose integral is path dependent. It is most often used in thermodynamics to express changes in path dependent quantities such as heat and work, but is defined more generally with ...

. Infinitesimal changes in a process function may be integrated, but the integral between two states depends on the particular path taken between the two states, whereas the integral of a state function is simply the difference of the state functions at the two points, independent of the path taken. In general, a process function may be either holonomic or non-holonomic. For a holonomic process function, an auxiliary state function (or integrating factor) may be defined such that is a state function. For a non-holonomic process function, no such function may be defined. In other words, for a holonomic process function, may be defined such that is an exact differential. For example, thermodynamic work is a holonomic process function since the integrating factor (where is pressure) will yield exact differential of the volume state function . The

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...

as stated by Carathéodory essentially amounts to the statement that heat is a holonomic process function since the integrating factor (where is temperature) will yield the exact differential of an entropy state function .

References

See also