Search results
Results From The WOW.Com Content Network
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.
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system [1] (e.g. gas, liquid, solid, crystal, or emulsion), not the path which ...
In the aircraft example, the observer on the ground will observe unsteady flow, and the observers in the aircraft will observe steady flow, with constant streamlines. When possible, fluid dynamicists try to find a reference frame in which the flow is steady, so that they can use experimental methods of creating streaklines to identify the ...
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 ...
A path from a point to a point in a topological space is a continuous function from the unit interval [,] to with () = and () =. A path-component of X {\displaystyle X} is an equivalence class of X {\displaystyle X} under the equivalence relation which makes x {\displaystyle x} equivalent to y {\displaystyle y} if and only if there is a path ...
The Cauchy's integral theorem states that if is a simply connected open subset of the complex plane, and : is a holomorphic function, then has an antiderivative on , and the value of every line integral in with integrand depends only on the end points and of the path, and can be computed as () ().
A curve in a topological space is a continuous function: from a non-empty and non-degenerate interval. A path in is a curve : [,] whose domain [,] is a compact non-degenerate interval (meaning < are real numbers), where () is called the initial point of the path and () is called its terminal point.
A path from a point x to a point y in a topological space X is a continuous function f from the unit interval [0,1] to X with f(0) = x and f(1) = y. A path-component of X is an equivalence class of X under the equivalence relation, which makes x equivalent to y if there is a path from x to y. The space X is said to be path-connected (or ...