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The distinction between intensive and extensive properties has some theoretical uses. For example, in thermodynamics, the state of a simple compressible system is completely specified by two independent, intensive properties, along with one extensive property, such as mass. Other intensive properties are derived from those two intensive variables.
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 independent variable (X-axis) is time and the dependent variable (Y-axis) is temperature. [1] Below is an example of a cooling curve used in castings. The initial point of the graph is the starting temperature of the matter, here noted as the "pouring temperature".
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 ...
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 ...
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. In electronic/electrical circuits, the voltages of the nodes and the currents through components in the circuit ...
It is also possible for other sets of phases to form a triple point, for example in the water system there is a triple point where ice I, ice III and liquid can coexist. If four phases of a pure substance were in equilibrium (P = 4), the phase rule would give F = −1, which is meaningless, since there cannot be −1 independent variables. This ...
If the rank of the matrix is C, then there are C linearly independent vectors, and the remaining N-C vectors can be obtained by adding up multiples of those vectors. The chemical species represented by those C vectors are components of the system. [3] If, for example, the species are C (in the form of graphite), CO 2 and CO, then