Volumetric expansion parameter

Since there is a change in the number of moles on reaction, the volumetric expansion parameter d will be nonzero. Consequently,... 

The volumetric expansion parameter S may thus be taken as 0.9675. The product distribution will vary somewhat with temperature, but the stoichiometry indicated above is sufficient for preliminary design purposes. (We should also indicate that if one s primary goal is the production of ethylene, the obvious thing to do is to recycle the propylene and ethane and any unreacted propane after separation from the lighter components. In such cases the reactor feed would consist of a mixture of propane, propylene, and ethane, and the design analysis that we will present would have to be modified. For our purposes, however, the use of a mixed feed would involve significantly more computation without serving sufficient educational purpose.)... 

Regressed Volumetric Thermal Expansion Parameters for Hydrate Volume (Divide by 3 to Get Linear Thermal Expansion Parameters)... 

The standard hydrates of si, sll, and sH were assumed to be the empty hydrates of methane, propane, and methane + neohexane, respectively. While the thermal expansion parameters are the same for the real and standard hydrates, the compressibility parameter and standard volume are not. The volumetric compressibilty of the standard hydrates of si, sll, and sH are 3E-5,3E-6, and 3E-7,... 

In the Multigrain model, fractured catalyst microparticles are produced during the polymerization and uniformly dispersed in the polymer each of these particles behaves as a micro Solid core and diffusion within them, as well as in the interstices between them, can take place. In the Polymeric flow model the catalyst microparticles are dispersed in a polymer continuum and move outward in proportion to the volumetric expansion due to polymerization only one value of diffusivity is considered. Both these models predict significant MWD broadening due to mass transfer limitations (Q , 9 for polypropylene in the Polymeric flow model) on the basis of mathematical calculations carried out assuming reasonable values of the kinetic and physical parameters. 

Calculate an estimate of the polymer-solvent interaction parameter (x) and the relative volumetric expansion (a ) of the polymer in each solvent. [Polymer density = 0.960 g/cm ]... 

The subscripts on the usual process parameters indicate the positions in the process to which these parameters refer. The kinetics of yeast growth can be described by a Monod rate expression with = 0.625 h and Kg = 2 g/L. Cell death and cell maintenance effects are negligible, as is formation of products other than yeast cells. The yield coefficient x/s is 0.44. The effluent from the bioreactor flows directly to a membrane filtration apparams. The membrane is completely permeable to the substrate, so the concentrations of the substrate in the CSTBR, the effluent from the bioreactor, and the permeate from the membrane and in the recycle stream are all identical. The membrane rejects a substantial proportion of the yeast cells so that the ratio of the concentration of yeast in the recycle stream is a factor of 4 larger than that in the effluent from the CSTBR. Volumetric expansion and contraction effects may be considered negligible. 

These parameters ean be calculated if factors of die volumetric expansion, isothermal eompressibility, thermal capacity of a solvent and enthalpy of mixing of solution components are known. 

The experimental data usually give the specific heat at constant pressure cP. Theories usually refer to the specific heat at constant volume cv. The specific heat cP is greater than cv by a factor (1 + jgT), where f5 is the volumetric coefficient of thermal expansion and yG is the so-called Griineisen parameter ... 

Corrections required when weighing volumetric flasks are somewhat different than straight volumetric readings. Both single- and double-pan balances have four common parameters which can affect the accurate weighing of liquids, but the single-pan balance has one separate parameter of its own. The common parameters are water density, glass expansion, and the buoyancy effect. 

This constant wo characterises the initial volumetric flow rate referring to a unit cross-sectional foam area. A rigorous analytical dependence of the constant wq on the structural parameters of a low expansion ratio foam and the properties of the solution (dp IdH, H, r, R, n, a) has not been derived, so that this constant cannot be calculated. 

Foam films are usually used as a model in the study of various physicochemical processes, such as thinning, expansion and contraction of films, formation of black spots, film rupture, molecular interactions in films. Thus, it is possible to model not only the properties of a foam but also the processes undergoing in it. These studies allow to clarify the mechanism of these processes and to derive quantitative dependences for foams, O/W type emulsions and foamed emulsions, which in fact are closely related by properties to foams. Furthermore, a number of theoretical and practical problems of colloid chemistry, molecular physics, biophysics and biochemistry can also be solved. Several physico-technical parameters, such as pressure drop, volumetric flow rate (foam rotameter) and rate of gas diffusion through the film, are based on the measurement of some of the foam film parameters. For instance, Dewar [1] has used foam films in acoustic measurements. The study of the shape and tension of foam bubble films, in particular of bubbles floating at a liquid surface, provides information that is used in designing pneumatic constructions [2], Given bellow are the most important foam properties that determine their practical application. The processes of foam flotation of suspensions, ion flotation, foam accumulation and foam separation of soluble surfactants as well as the treatment of waste waters polluted by various substances (soluble and insoluble), are based on the difference in the compositions of the initial foaming solution and the liquid phase in the foam. Due ro this difference it is possible to accelerate some reactions (foam catalysis) and to shift the chemical equilibrium of some reactions in the foam. The low heat... 

Natural convection occurs when a fluid is in contact with a solid surface of different temperature. Temperature differences create the density gradients that drive natural or free convection. In addition to the Nusselt number mentioned above, the key dimensionless parameters for natural convection include the Rayleigh number Ra = p AT gx3/ va and the Prandtl number Pr = v/a. The properties appearing in Ra and Pr include the volumetric coefficient of expansion p (K-1) the difference AT between the surface (Ts) and free stream (Te) temperatures (K or °C) the acceleration of gravity g(m/s2) a characteristic dimension x of the surface (m) the kinematic viscosity v(m2/s) and the thermal diffusivity a(m2/s). The volumetric coefficient of expansion for an ideal gas is p = 1/T, where T is absolute temperature. For a given geometry,... 

Volumetric coefficient of expansion in general. With subscripts C, M. PB, PS, P composite, matrix, polybutadiene, polystyrene, particle, respectively Mean distance between crazes in the volume With subscripts. A, B solubility parameter With subscripts. A, B, solubihty parameter... 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

The supercooled liquid catastrophe, if it exists, would necessarily be associated with diverging fluctuations in the structural order parameter F. This stems from the fact that the Y surface develops a vanishing curvature in the F direction as this endpoint is approached. Because the bicyclic octamer elements are bulky, fluctuations in their coiKentration amount to density fluctuations. Diverging density fluctuations then imply diverging isothermal compressibility. Furthermore the infinite slope of the metastable liquid locus at its endpoint implies the divergence of thermal expansion. Potential energy fluctuations remain essentially normal, so constant-volume heat capacity remains small. But the volumetric divergence creates an unbounded constant-pressure heat capacity. 

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