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In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
The number of components (C) is the number of chemically independent constituents of the system, i.e. the minimum number of independent species necessary to define the composition of all phases of the system. [3] The number of degrees of freedom (F) in this context is the number of intensive variables which are independent of each other.
The IUPAC definitions do not consider such cases. [5] Some intensive properties do not apply at very small sizes. For example, viscosity is a macroscopic quantity and is not relevant for extremely small systems. Likewise, at a very small scale color is not independent of size, as shown by quantum dots, whose color depends on the size of the "dot".
The same is true for intervening variables (a variable in between the supposed cause (X) and the effect (Y)), and anteceding variables (a variable prior to the supposed cause (X) that is the true cause). When a third variable is involved and has not been controlled for, the relation is said to be a zero order relationship. In most practical ...
The number of components represents the minimum number of independent chemical species necessary to define the composition of all phases of the system. [ 2 ] Calculating the number of components in a system is necessary when applying Gibbs' phase rule in determination of the number of degrees of freedom of a system.
The remaining variable, as well as other quantities such as the internal energy and the entropy, would be expressed as state functions of these three variables. The state functions satisfy certain universal constraints, expressed in the laws of thermodynamics , and they depend on the peculiarities of the materials that compose the concrete system.
The instantaneous rate of change is a well-defined concept that takes the ratio of the change in the dependent variable to the independent variable at a specific instant. This is an image of vials with different amounts of liquid. A continuous variable could be the volume of liquid in the vials. A discrete variable could be the number of vials.
Variables may be of many types; real or integer numbers, Boolean values or strings, for example. The variables represent some properties of the system, for example, the measured system outputs often in the form of signals, timing data, counters, and event occurrence. The actual model is the set of functions that describe the relations between ...