thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

, a quantity that is well defined so as to describe the path of a process through the equilibrium state space of a

thermodynamic system A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics. Thermodynamic systems can be passive and active according to internal processes. According to inter ...

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

heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...

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,

and

arc length Arc length is the distance between two points along a section of a curve. Development of a formulation of arc length suitable for applications to mathematics and the sciences is a problem in vector calculus and in differential geometry. In the ...

. In contrast to path functions, state functions are independent of the path taken. Thermodynamic state variables 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 (infinitesimal), 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 som ...

, while is not, it is an inexact differential. 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 (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...

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