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The path can be specified by noting the values of the state parameters as the system traces out the path, whether as a function of time or a function of some other external variable. For example, having the pressure P ( t ) and volume V ( t ) as functions of time from time t 0 to t 1 will specify a path in two-dimensional state space.
Examples of path functions include work, heat and arc length. 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.
The difference between initial and final states of the system's internal energy does not account for the extent of the energy interactions transpired. Therefore, internal energy is a state function (i.e. exact differential), while heat and work are path functions (i.e. inexact differentials) because integration must account for the path taken.
Whether carried out reversible or irreversibly, the net entropy change of the system is zero, as entropy is a state function. During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. Process quantities (or path quantities), such as heat and work are process dependent.
In thermodynamics, a state variable is an independent variable of a state function. Examples include internal energy , enthalpy , temperature , pressure , volume and entropy . Heat and work are not state functions, but process functions .
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.
An example of a cycle of idealized thermodynamic processes which make up the Stirling cycle. A quasi-static thermodynamic process can be visualized by graphically plotting the path of idealized changes to the system's state variables. In the example, a cycle consisting of four quasi-static processes is shown.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.