Fixed mass

We assume that the nuclei are so slow moving relative to electrons that we may regard them as fixed masses. This amounts to separation of the Schroedinger equation into two parts, one for nuclei and one for electrons. We then drop the nuclear kinetic energy operator, but we retain the intemuclear repulsion terms, which we know from the nuclear charges and the intemuclear distances. We retain all terms that involve electrons, including the potential energy terms due to attractive forces between nuclei and electrons and those due to repulsive forces... 

The reactor feed may be preheated and the feed pressure may alter. The volumetric flowrate of gases depends on the reactor temperature and pressure at fixed mass flowrate. In many cases, the feed is liquid at room temperature, while the reaction mixture is a gas at the higher temperature in the reactor. In these instances, the performance of the reactor is represented as conversion and selectivity against the liquid hourly space velocity (LHSV). This is defined as... 

Boyle s Law. At constant temperature (T), the volume (V) of a fixed mass of an ideal gas is inversely proportional to the absolute pressure (P). That is,... 

The law of multiple proportions This law, formulated by Dalton himself, was crucial to establishing atomic theory. It applies to situations in which two elements form more than one compound. The law states that in these compounds. the masses of one element that combine with a fixed mass of the second element are in a rath of small whole numbers. 

The most complex problem of this type requires you to determine the simplest formula of a compound given only the raw data obtained from its analysis. Here, an additional step is involved you have to determine the masses of the elements present in a fixed mass of the compound (Example 3.6). 

Strategy Start with a fixed mass of solution such as one hundred grams. First calculate the masses of H20 and H202, then the number of moles, and finally the mole fraction of H202. 

The fixed mass (M) and fixed number (N) reference frames can also be defined. The mutual diffusion is equally well described in any of these three coordinate systems ... 

The present paper tests the assumed original and enhancement mechanisms with rates and conversions for a broad range of contaminants measured under a fixed mass concentration (50 mg/m ) feed condition. The plots compared are reaction rates vs. (1) dark adsorption, Ot. (2) second order rate constant for (OH ) (TCE absent) or (Cl ) (TCE present), and (3) the product of these gas phase second order rate constant times the reactant dark coverage. Where a second order gas phase rate constant was not available, we estimated its value from correlations of kci vs. koH for tke same class of compounds. 

For a fixed mass load of contaminant for the processes below the pinch, decrease the volumetric flowrate of the processes below the pinch, thus increasing concentrations. 

Secondly, the network layout showed in Fig. 12.7 shows that 12.5 t of water should be supplied to Process 3, instead of 25 t stipulated in the problem specification. This can only be true if this process does not have flowrate constraints, but has a fixed mass load. The assumption of fixed mass loads was never mentioned in the analysis. This variation of flowrate is contrary to the assumption made in targeting. During targeting it was implicitly assumed that the flowrates were fixed as shown by the calculation of water demand in each of the time subintervals. 

Ans. The ratio of the mass of one element in one compound to the mass of that element in the other compound—for a fixed mass of the other element—must be in a ratio of small whole numbers. Let us calculate the mass of oxygen in the two compounds per gram of iron. That is, the fixed mass will be l.OOg Fe. 

For a fixed mass, the conservation of linear momentum is equivalent to Newton s second law ... 

Suppose that, at any time t, the mass of stars within a fixed mass coordinate m is s(m, t) and that the gas is confined within a decreasing mass coordinate ma(t). We make the simplifying but reasonable assumption that, within ma t), the radial distributions of stars and of the star formation rate are the same. Furthermore, we assume the Ansatz... 

Now the mass of phosphorus for both reactions is fixed at 1.000 g. Next, we will divide each amount of chlorine by the fixed mass of phosphorus with which they are combined. This gives... 

Consider the instantaneous release of a fixed mass of material, Q, into an infinite expanse of air (a ground surface will be added later). The coordinate system is fixed at the source. Assuming no reaction or molecular diffusion, the concentration C of material resulting from this release is given by the advection equation... 

A control volume is a volume specified in transacting the solution to a problem typically involving the transfer of matter across the volume s surface. In the study of thermodynamics it is often referred to as an open system, and is essential to the solution of problems in fluid mechanics. Since the conservation laws of physics are defined for (fixed mass) systems, we need a way to transform these expressions to the domain of the control volume. A system has a fixed mass whereas the mass within a control volume can change with time. 

The law that now bears his name can be stated as, The ratio of volume and temperature for a fixed mass of gas remains constant , provided the external pressure is not altered. 

As shown above in (6.162), the Lagrangian fluid-particle PDF can be related to the Eulerian velocity, composition PDF by integrating over all initial conditions. As shown below in (6.168), for the Lagrangian notional-particle PDF, the same transformation introduces a weighting factor which involves the PDF of the initial positions y) and the PDF of the current position /x.(x t). If we let V denote a closed volume containing a fixed mass of fluid, then, by definition, x, y e V. The first condition needed to reproduce the Eulerian PDF is that the initial locations be uniform ... 

If the reaction system is treated as a closed system of fixed mass, only the species and energy equations need to be considered. Consider a system with total mass... 

Finally, a number of experimental studies have been conducted in a pressure range where the polymeric solution could boil. The vapor bubbles thus created would provide a much larger surface area for mass transfer than the surface area of the wiped film alone. And therefore, for fixed values of the diffusivity and the driving force, predicted values for mass transfer rates would be substantially lower than the measured values. Conversely, for a fixed mass transfer rate and driving force, use of the wiped film surface area alone would require unusually high values of the diffusivity in order to obtain agreement between theory and experiment. 

Calculation of N. The composited samples are formed by combining a specified fixed mass of tissue (e.g., 1 gram) from each specimen. The entire composited sample is then extracted down to a prespecified final extract volume. Each analytical determination involves an injection of a small amount of the extract into the analytical Instrument. 

As shown in Figure 6.13b, Q1 and Q3 are both scanning from low to high mass but with a fixed mass difference that corresponds to the mass of the neutral molecule lost during CID. This can be especially useful when analysing the same class of compounds or for group-specific detection. 

Still curled up at the heart of the parent cloud, the stellar embryos attract more matter in order to embark upon the visible phase of an object of fixed mass in hydrostatic equilibrium. They then disperse any surrounding matter and begin their own lives as free and independent stars. 

Lattice Points positions in a unit cell occupied by atom, molecules, or ions Law of Definite Proportion law that states that different samples of the same compound always contain elemental mass percentages that are constant Law of Mass Action mathematical expression based on the ratio between products and reactants at equilibrium, an equation to determine the equilibrium rate constant Law of Multiple Proportions law that states when two elements combine to form more than one compound that the mass of one element compared to the fixed mass of... 

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