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Assuming that the temperature T is an intensive quantity, i.e., a single-valued, continuous and differentiable function of three-dimensional space (often called a scalar field), i.e., that = (,,) where x, y and z are the coordinates of the location of interest, then the temperature gradient is the vector quantity defined as
It is possible to envision three-dimensional (3D) graphs showing three thermodynamic quantities. [12] [13] For example, for a single component, a 3D Cartesian coordinate type graph can show temperature (T) on one axis, pressure (p) on a second axis, and specific volume (v) on a third. Such a 3D graph is sometimes called a p–v–T diagram. The ...
The expression (/) represents the fraction of the molecules present in a gas which have energies equal to or in excess of activation energy at a particular temperature. In almost all practical cases, E a ≫ R T {\displaystyle E_{\text{a}}\gg RT} , so that this fraction is very small and increases rapidly with T {\displaystyle T} .
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.This is often written as = or =, where = = is the Laplace operator, [note 1] is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and (,,) is a twice-differentiable real-valued function.
The unit circle can be specified as the level curve f(x, y) = 1 of the function f(x, y) = x 2 + y 2.Around point A, y can be expressed as a function y(x).In this example this function can be written explicitly as () =; in many cases no such explicit expression exists, but one can still refer to the implicit function y(x).
A three-dimensional surface, whose contour graph is below. A two-dimensional contour graph of the three-dimensional surface in the above picture. A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.
A key to understanding the greenhouse effect is Kirchhoff's law of thermal radiation. At any given wavelength the absorptivity of the atmosphere will be equal to the emissivity. Radiation from the surface could be in a slightly different portion of the infrared spectrum than the radiation emitted by the atmosphere.