Dimensionless energy

Characteristic Lennard-Jones energy Dimensionless Dimensionless... 

AE net sample adsorption energy (dimensionless free energy of ad-... 

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

Figure A2.2.1. Heat capacity of a two-state system as a function of the dimensionless temperature, lc T/([iH). From the partition fimction, one also finds the Helmholtz free energy as...

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

As is evident from the fomi of the square gradient temi in the free energy fiinctional, equation (A3.3.52). k is like the square of the effective range of interaction. Thus, the dimensionless crossover time depends only weakly on the range of interaction as In (k). For polymer chains of length A, k A. Thus for practical purposes, the dimensionless crossover time is not very different for polymeric systems as compared to the small molecule case. On the other hand, the scaling of to is tln-ough a characteristic time which itself increases linearly with k, and one has... 

In this equation, represents the rate of energy dissipation per unit mass of fluid. In pulsed and reciprocating plate columns the dimensionless proportionahty constant K in equation 38 is on the order of 0.3. In stirred tanks, the proportionaUty constant has been reported as 0.024(1 + 2.5 h) in the holdup range 0 to 0.35 (67). The increase of drop si2e with holdup is attributed to the increasing tendency for coalescence between drops as the concentration of drops increases. A detailed survey of drop si2e correlations is given by the Hterature (65). 

According to equation 132, is the residual Gibbs energy, G. The dimensionless mXio fjP is a new property called the fugacity coefficient, ( ). ... 

The difference on the left is the partial excess Gibbs energy G y the dimensionless mXio J on the right is called the activity coefficient of species i in solution, y. Thus, by definition. 

For a given fixed flow rate Q = Vbh, and channel width profile b(x), Eq. (6-56) may be integrated to determine the liquid depth profile h(x). The dimensionless Fronde number is Fr = VVg/j. When Fr = 1, the flow is critical, when Fr < 1, the flow is subcritical, and when Fr > 1, the flow is supercritical. Surface disturbances move at a wave velocity c = V they cannot propagate upstream in supercritical flows. The specific energy Ejp is nearly constant. 

Maximum allowable values of the capacity parameter are for a flooding condition and are designated C,i,f. Experimental values have been correlated against a dimensionless flow parameter Flg as shown in Fig. 14-25. The flow parameter represents a ratio of liquid to vapor kinetic energies ... 

The Tempered activation energy , is the activation energy divided by R, the gas constant, and is dimensionless. It will be shown here with a superscript T, e.g. 10 000. ... 

The objectives are not realized when physical modeling are applied to complex processes. However, consideration of the appropriate differential equations at steady state for the conservation of mass, momentum, and thermal energy has resulted in various dimensionless groups. These groups must be equal for both the model and the prototype for complete similarity to exist on scale-up. 

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