gibb s free energy differential enthalpy differential entropy and integral entropy

... tempering, and this is suspected to affect the crystal size, mass (number), strengths and adequacy of the fat crystals formed and thus possible defects in structure and product shelf stability ... manufacture are consistent and would yield the desired mechanical and sensory qualities during post-processing handling, supply chain management and consumption Understanding these processes is important ... brown spots (Figure 7) The observed whitish appearance on surfaces and internal peripheries appear to be mixtures of fat and sugar crystals, and the small brown spots, cocoa solids These whitish spots...

Ngày tải lên: 02/04/2014, 15:05

... r sin x1 cos x2 y3 = r sin x1 sin x2 cos x3 yn-1 = r sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 sin xn-1 cos xn yn+1 = r sin x1 sin x2 sin x3 sin x4 sin xn-1 sin ... xn) 42 3 = (0, 0, -r sin x sin x sin x , r sin x sin x cos x cos x , x r sin x1 sin x2 cos x3 sin x4 sin xn-1 cos xn, r sin x1 sin x2 cos x3 sin x4 sin xn-1 sin xn), and so on g11 g22 g33 ... and < xn < 2, given by y1 = cos x1 y2 = sin x1 cos x2 y3 = sin x1 sin x2 cos x3 yn-1 = sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = sin x1 sin x2 sin x3 sin x4 sin xn-1 cos xn yn+1 = sin x1 sin...

Ngày tải lên: 17/03/2014, 14:28

... H Hyers, G Isac, and Th M Rassias, Stability of Functional Equations in Several Variables, Birkh¨ user, Boston, Mass, USA, 1998 a [5] D H Hyers and Th M Rassias, “Approximate homomorphisms,” Aequationes ... ρ1 is any positive number and C is some constant which depends on ρ0 This completes the proof of our theorem Example In this section, our task is to show that there certainly exist functions y(x) ... functions Inhomogeneous Bessel equation A function is called a Bessel function if it satisfies the Bessel differential equation x2 y (x) + xy (x) + x2 − ν2 y(x) = (2.1) The Bessel equation plays a...

Ngày tải lên: 22/06/2014, 11:20

... cos x2 sin x3 … sin xn-1 sin xn) ∂ 3 = (0, 0, -r sin x sin x sin x , r sin x sin x cos x cos x , ∂x r sin x1 sin x2 cos x3 sin x4… sin xn-1 cos xn, r sin x1 sin x2 cos x3 sin x4 … sin xn-1 sin ... cos x y2 = r sin x1 cos x2 y3 = r sin x1 sin x2 cos x3 … yn-1 = r sin x1 sin x2 sin x3 sin x4 … cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 … sin xn-1 cos xn yn+1 = r sin x1 sin x2 sin x3 sin ... x cos x , r cos x sin x cos x , , ∂x r cos x1 sin x2… sin xn-1 cos xn, r cos x1 sin x2 … sin xn-1 sin xn) ∂ 2 n-1 cos xn, = (0, -r sin x sin x , , r sin x cos x sin x … sin x ∂x r sin x1...

Ngày tải lên: 12/08/2014, 16:20

... = a to t Then s is an invertible function of t, and, using s as a parameter, ||dxi/ds||2 is constant, and equals if C is space-like and -1 if it is time-like Conversely, if t is any parameter ... reason as above) (a) says that we measure the world line C as representing a particle traveling with light speed, and (b) says that we measure ordinary length in the usual way This motivates the ... det(gij) is nowhere zero Show that the resulting inverse (of matrices) gij is a type (2, 0) tensor (Note that it l must satisfy gijgkl = ©k ©j ) i (Index lowering and raising) Show that, if Rabc is a...

Ngày tải lên: 12/08/2014, 16:20

... Christoffel Symbols of the First Kind Christoffel Symbols of the Second Kind Neither of these gizmos are tensors, but instead transform as follows (Which you will prove in the exercises!) Transformation ... ys,qr ys,p + ys,pq ys,r gpq,r = ys,rp ys,q + ys,qr ys,p Note that each term on the right occurs twice altogether as shown by the boxes This permits us to solve for the completely boxed term ys,pq ... correctly This allows us to say whether a field is parallel and of constant length by seeing whether this quantity vanishes This claim is motivated by the following Proposition 8.3 (Parallel Fields of...

Ngày tải lên: 12/08/2014, 16:20

... whose first curvature is zero is called a geodesic Thus, a geodesic is a curve that satisfies the system of second order differential equations    i  dxp dxq d2xi   + pq ds ds =   ds ... d “P, T‘ = (±1) = 0, ds as asserted Local Flatness, or “Local Inertial Frames” In “flat space” Es all the Christoffel symbols vanish, so the following question arises: Question Can we find a chart ... coordinate system) such that the Christoffel symbols vanish—at least in the domain of the chart? Answer This is asking too much; we shall see later that the derivatives of the Christoffel symbols give...

Ngày tải lên: 12/08/2014, 16:20

... that this field is only defined along C, but (I) still makes sense.) Why? because j i h d2xj D(dx /ds) j dx dx = + ¶i h , Ds ds ds ds which must be zero for a geodesic (b) Proper Coordinates in ... coordinate system, so we choose the unique local inertial one there, because in the eyes of the observer, spacetime should be flat.) Question Does parallel transport preserve the relationship of these ... gbiRaicd Substituting the first of the above (boxed) formulas into the second, and using symmetry of the second derivatives and the metric tensor, we find (exercise set) Covariant Curvature Tensor...

Ngày tải lên: 12/08/2014, 16:20

... T is a symmetric tensor Definition 11.4 Classically, a fluid has no viscosity if its stress tensor is diagonal in an MCFR (viscosity is a force parallel to the interfaces) Thus, for a viscosity -free ... is the mass energy density of the fluid p is the pressure ui is its 4-velocity Note that the scalars in this definition are their physical magnitudes as measured in a MCRF 97 Conservation Laws ... å2F is the resultant force on the scaled version of the prism, whereas its mass is proportional to å3 Thus its acceleration is proportional to 1/å (using Newton 's law) This means that, as å becomes...

Ngày tải lên: 12/08/2014, 16:20

... constant ¿ mass density where ® is the mass density and G is a constant (The divergence theorem then gives the more familiar F = Ô˙ = GM/r2 for a spherical source of mass M—see the exercise set.) ... child to this day.† We shall set it equal to zero Solution of Einstein 's Equations for Static Spherically Symmetric Stars In the case of spherical symmetry, we use polar coordinates (r, ø, ˙, ... gab,i and gab, and must also be symmetric (since T is) Examples of such a tensors are the Ricci tensors Rab, gabR, as well as gab Let us take a linear combination as our candidate: Rab + µgabR +...

Ngày tải lên: 12/08/2014, 16:20

... as well, and so 1-2M/r is positive, and never zero (If r ≤ 2M, we are inside the star, and the Schwarzschild metric no longer applies.) r rs r = 2M Case (Extremely Dense Stars) Radius of the star, ... = (grk ,s + gks,r - gsr,k) PrPk d† But the sum of the second and third terms in parentheses is skew-symmetric in r and k, whereas the term outside is symmetric in them This results in them canceling ... when 2M = r, and we look at two cases Case (Not-So-Dense Stars) Radius of the star, rs > 2M If we recall that the Schwarzschild metric is only valid for outside a star; that is, r > rs, we find...

Ngày tải lên: 12/08/2014, 16:20

... neutrons (and neutrinos which are nearly massless and noninteracting) A sufficiently dense star is unstable against such an interaction and all electrons and protons are converted to neutrons leaving ... induces compression Thus, if the total energy E is negative, the star will continue to collapse (with an ever increasing inward force) unless some other force intervenes These behaviors are suggested ... is attractive -energy decreases with decreasing R We would like to express Eg in terms of N, like Ee -this will make the resulting expressions easier to adapt to neutron stars later on The mass...

Ngày tải lên: 12/08/2014, 16:20

... Chemistry: A Molecular Approach ∆Ssurroundin gs = − ∆H system T 26 Gibbs Free Energy, G ΔSuniverse= ΔSsurroundings+ ΔSsystem = - ΔHsystem / T + ΔSsystem -TΔSuniverse = ΔHsystem - T ΔSsystem = ΔGsystem ... for irreversible (nonspontaneous) process ∆Suniv < • ∆Suniverse = ∆Ssystem + ∆Ssurroundings • if the entropy of the system decreases, then the entropy of the surroundings must increase by a larger ... ΔGsystem ΔG is the change in free energy for the system ΔGosystem = ΔHosystem - TΔSosystem (standard state) ΔGorxn from ΔGof and from ΔHorxn and ΔSorxn ΔGorxn= ΔGfo(products) - ΔGfo(reactants)...

Ngày tải lên: 28/11/2013, 01:12

... oil Safe to store and handle, biodegradable, won't spontaneously ignite, and non-toxic no yes yes no yes yes yes yes yes yes yes no yes yes no yes yes no yes yes no no no yes no yes yes no yes ... Tested and documented by U .S universities Possible substitute for home heating oil in furnaces Can be used in Petromax brand and similar lanterns and stoves no no yes yes no no yes yes yes yes ... glycerin soap You can scent it with the fragrance of your choice, add other soap agents as desired, or just use it as it is This soap is especially good for cleaning grease off your hands and cleaning...

Ngày tải lên: 27/01/2014, 14:20

... Climate science is increasingly solid on fundamental issues of human influence and association with emissions and land use Industry, the U .S Congress, and most state governments accept this, and the ... emissions Two types of market-based approaches were discussed: (1) a cap -and- trade system, in which the government sets an emissions limit and issues tradable permits for the amount of emissions ... of society s essential physical assets and natural resources and to enhance the related social assets of safety and security of individuals in transit and in their workplaces and communities The...

Ngày tải lên: 06/03/2014, 21:20

... and its physical applications (2nd edition), J MADORE 258 Sets and proofs, S. B COOPER & J.K TRUSS (eds) 259 Models and computability, S. B COOPER & J TRUSS (eds) 260 Groups St Andrews 1997 in Bath ... (2008) considered unsteady flows of incompressible fluids whose viscosity depends on the temperature, shear-rate and pressure Such a fluid model is markedly different from the classical incompressible ... inequalities as it overcomes obstacles coming from the usual methods One needs neither compactness of the dynamics which results from the second energy inequality nor asymptotic compactness, see Boukrouche...

Ngày tải lên: 14/03/2014, 10:20

... activities [338] Nonetheless, the reaction mechanism of PDEs is still not fully understood, particularly on the issues of concerted and stepwise pathways via SN2- or SN1-like processes In this work, ... productrelease step This idea is consistent with the structural facts that His234 is absolutely conserved across the PDE family and that the three surrounding residues (Tyr233, His278 and Glu413; see ... potentials, and quantum chemical minimizations to understand various properties of PDEs [2638] These studies were performed either as ground state stable species in MD simulations, or as active site...

Ngày tải lên: 14/03/2014, 23:20

... theorem falls into two steps Step 1: Assume that y(t) is the solution of Eq.(9), for each sufficiently large s ≥ 0, y (s) ∈ E we set ∞ x (s) = y (s) + V (s − τ )f (τ, y(τ + θ))dτ s Therefore, the solution ... equations, Scientis publishing house Anma-Ata, 1974 (Russian) [13] N.T Hoan, Asymptotic equivalence of systems of differential equations, IZV.Acad Nauk ASSR (1975) 35 (Russian) [14] C.K Sung, H.G ... ϕ(t); −h exists solely It can be written in the form: t x(t) = T (t)ϕ(0) + µ T (t − s) f (s, x (s + θ))ds, t ≥ 0 Thus t x(t) T (t) ϕ(0) + µ T (t − s) f (s, x (s + θ)) ds, By using assumptions (5), (6),...

Ngày tải lên: 22/03/2014, 11:20

... cupboards and book-shelves; here and there she saw maps and pictures upon pegs She took down a jar from one of the shelves as she passed; it was labelled ‘ORANGE MARMALADE’, but to her great disappointment ... I suppose.’ So she swallowed one of the cakes, and was delighted to find that she began shrinking directly As soon as she was small enough to get through the door, she ran out of the house, and ... this before, never! And I declare it s too bad, that it is!’ As she said these words her foot slipped, and in another moment, splash! she was up to her chin in salt water Her first idea was that...

Ngày tải lên: 24/03/2014, 00:20

... y2 = sin x1 cos x2 y3 = sin x1 sin x2 cos x3 yn-1 = sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = sin x1 sin x2 sin x3 sin x4 sin xn-1 cos xn yn+1 = sin x1 sin x2 sin x3 sin x4 sin xn-1 sin xn ... r sin x1 cos x2 y3 = r sin x1 sin x2 cos x3 yn-1 = r sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 sin xn-1 cos xn yn+1 = r sin x1 sin x2 sin x3 sin x4 sin xn-1 sin ... r sin x1 sin x2 cos x3 yn-1 = r sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 sin xn-1 cos xn yn+1 = r sin x1 sin x2 sin x3 sin x4 sin xn-1 sin xn (d) The torus...

Ngày tải lên: 27/03/2014, 11:52