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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 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.
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 ...
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 .
is called a sample function, a realization, or, particularly when is interpreted as time, a sample path of the stochastic process {(,):}. [50] This means that for a fixed ω ∈ Ω {\displaystyle \omega \in \Omega } , there exists a sample function that maps the index set T {\displaystyle T} to the state space S {\displaystyle S} . [ 28 ]
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.
Let (Ω, Σ, P) be a probability space.Let X : I × Ω → S be a stochastic process, where the index set I and state space S are both topological spaces.Then the process X is called sample-continuous (or almost surely continuous, or simply continuous) if the map X(ω) : I → S is continuous as a function of topological spaces for P-almost all ω in Ω.
Path: a continuous set of branches traversed in the direction that they indicate. Forward path: A path from an input node to an output node in which no node is touched more than once. Loop: A path that originates and ends on the same node in which no node is touched more than once. Path gain: the product of the gains of all the branches in the ...