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The figure shows the schematic P-T diagram of a pure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known phases solid , liquid and vapor are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist.
The coordinate-independent definition of the square of the line element ds in an n-dimensional Riemannian or Pseudo Riemannian manifold (in physics usually a Lorentzian manifold) is the "square of the length" of an infinitesimal displacement [2] (in pseudo Riemannian manifolds possibly negative) whose square root should be used for computing curve length: = = (,) where g is the metric tensor ...
A simple application of dimensional analysis to mathematics is in computing the form of the volume of an n-ball (the solid ball in n dimensions), or the area of its surface, the n-sphere: being an n-dimensional figure, the volume scales as x n, while the surface area, being (n − 1)-dimensional, scales as x n−1.
The PES concept finds application in fields such as physics, chemistry and biochemistry, especially in the theoretical sub-branches of these subjects. It can be used to theoretically explore properties of structures composed of atoms, for example, finding the minimum energy shape of a molecule or computing the rates of a chemical reaction .
chemistry (Proportion of "active" molecules or atoms) Arrhenius number = Svante Arrhenius: chemistry (ratio of activation energy to thermal energy) [1] Atomic weight: M: chemistry (mass of one atom divided by the atomic mass constant, 1 Da) Bodenstein number: Bo or Bd
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1. The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ, is the area of a spherical cap on a unit sphere
The set of coordinates that define the position of a reference point and the orientation of a coordinate frame attached to a rigid body in three-dimensional space form its configuration space, often denoted () where represents the coordinates of the origin of the frame attached to the body, and () represents the rotation matrices that define the orientation of this frame relative to a ground ...
Extension per unit length unitless 1: Stress: σ: Force per unit oriented surface area Pa L −1 M T −2: order 2 tensor Surface tension: γ: Energy change per unit change in surface area N/m or J/m 2: M T −2: Thermal conductance κ (or) λ: Measure for the ease with which an object conducts heat W/K L 2 M T −3 Θ −1: extensive Thermal ...