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The last equality follows from the relation =, [29] together with = +. [18] All this means that every point on the line has the same values of g , p , T {\displaystyle g,p,T} , in particular the points B and F, which produces the Gibbs condition for material equilibrium g f = g g {\displaystyle g_{f}=g_{g}} as well as eqality of temperature and ...
The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant, P = constant or Helmholtz free energy F at T = constant, V = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (internal energy).
= (/),, where is not proportional to because depends on pressure. μ i = ( ∂ G / ∂ N i ) T , P {\displaystyle \mu _{i}=\left(\partial G/\partial N_{i}\right)_{T,P}} , where G {\displaystyle G} is proportional to N {\displaystyle N} (as long as the molar ratio composition of the system remains the same) because μ i {\displaystyle \mu _{i ...
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
This list of all two-letter combinations includes 1352 (2 × 26 2) of the possible 2704 (52 2) combinations of upper and lower case from the modern core Latin alphabet.A two-letter combination in bold means that the link links straight to a Wikipedia article (not a disambiguation page).
The space M n (H) ⊂ M 2n (C) is a real algebra, but it is not a complex subspace of M 2n (C). Multiplication (from the left) by i in M n (H) using entry-wise quaternionic multiplication and then mapping to the image in M 2n (C) yields a different result than multiplying entry-wise by i directly in M 2n (C).
In terms of the standard unit vectors i, j, k of Cartesian 3-space, these specific types of vector-valued functions are given by expressions such as = + + where f(t), g(t) and h(t) are the coordinate functions of the parameter t, and the domain of this vector-valued function is the intersection of the domains of the functions f, g, and h.
The lists and tables below summarize and compare the letter inventories of some of the Latin-script alphabets.In this article, the scope of the word "alphabet" is broadened to include letters with tone marks, and other diacritics used to represent a wide range of orthographic traditions, without regard to whether or how they are sequenced in their alphabet or the table.