Cube, conduction

Conductivity. The standard unit of conductance is electrolytic conductivity (formerly called specific conductance) k, which is defined as the reciprocal of the resistance of a 1-m cube of liquid at a specified temperature m— ]. See Table 8.33 and the definition of the cell constant. 

The term equivalent conductance A is often used to describe the conductivity of electrolytes. It is defined as the conductivity of a cube of solution having a cross-section of one square centimeter and containing one equivalent of dissolved electrolyte. 

However, even with the most advanced measuring and simulation tools, the most efficient methods are simple calculations that give an order-of-magnitude estimation of the influence of a phenomenon. Time constants for diffusion, heat conduction, and acceleration are very useful. For example, the time constant for diffusion Td = f/D is the time it takes to fill a cube of size I by diffusion, and the time for a particle to accelerate from zero velocity to approximately two-third of the velocity of the surrounding fluids is 118/j, where p[Pg.331]

In the above relationship p is an intrinsic property called the specific resistance (or resistivity) of the conductor. The definition of the specific resistance of any given conductor follows from this relationship. It is the resistance in ohms of a specimen of the material, 1 cm long and 1 cm2 in cross-sectional area (units ohm cm-1), the length being in the direction of the current and the cross-section normal to it. In other words, the specific resistance p of a conductor is the resistance of a cube of 1 centimeter edge. If the conductance is denoted by C = 1 /R, then the specific conductance (or conductivity) K, is given by JC= 1/a (units ohm-1 cm-1, mho cm-1, reciprocal ohm cm-1). Therefore, the relationship R = aL/A may be written as R = L/KA (units ohms) and the conductance can be expressed as C = 1/R = KA/l (units reciprocal ohms). 

The reactions were conducted according to a two factorial design with three variables, which contains experimental points at the edges and the center of a face-centered cube leading to 9 different experiments. Typically, the experiment at the center point is conducted at least 3 times to add degrees of freedom that allow the estimation of experimental error. Hence a total of 11 experiments are needed to predict the reaction rate within the parameter space. The parameter space for the catalysts to be prepared is shown in columns 2-4 in Table 1. 

It is important to note that in the molecular flow regime the conductance depends on the cube of the diameter of the tube and the — power of the molecular weight of the gas being pumped, but it is independent of the pressure. 

If two opposite faces of a cube, made from the substance to be examined, are maintained at temperatures (Tj) and (T2), the heat conductivities across the section of the cube (A) cm2 and (D) cm thick, the specific heat conductivity ... 

Difluorides such as PbF2 with the fluorite structure exhibit fast ion conduction due to facile F ion transport (Section 6.4.5). An interesting structure showing Li" conduction is that of LijN (Rabenau, 1978). Conduction is two-dimensional. Cooperative basal plane excitations involving the rotation of six Li ions by 30 about a common ion to edge positions (positions midway between ions in the Li2N layer) seem to be responsible for conduction in this nitride. In the fluorite structure, a rotation by 45 of a single cube of F ions seems to be involved. The Zintl alloy LiAl is also a lithium-ion conductor. 

Fig. 1.19 Conductivity a/(e2lha) as a function of WjV (12 V0/B in our notation) calculated for a finite cube of varying size by Kramer et al. (1981). The cube side N is from 5 to 14...

We do not know how quickly the factor g comes into play as V0 approaches 0.6B. Figure 1.19 shows some results of Kramer et al (1981) on the conductivity calculated for finite cubes. Extrapolation to V0/B=0.6 suggests that al(e2lha) must be about 0.2, instead of the value 0.3 that is obtained for g= 1. 

Because the surface of rubbers may conduct electricity more easily than the bulk of the material, it is usual to distinguish between volume resistivity and surface resistivity. Volume resistivity is defined as the electrical resistance between opposite faces of a unit cube, whereas surface resistivity is defined as the resistance between opposite sides of a square on the surface. Resistivity is occasionally called specific resistance. Insulation resistance is the resistance measured between any two particular electrodes on or in the rubber and, hence, is a function of both surface and volume resistivities and of the test piece geometry. Conductance and conductivity are simply the reciprocals of resistance and resistivity respectively. 

Two electrodes. 1 centimeter square, located on opposite interior faces of a hollow cube. I centimeter on an edge, would have a cell constant of 1/cm a measured conductance of tUO microsierneris at 25 C would indicate a conductivity of 100 microsiemens/cm (10 milUsiemens/m) at 25°C. 

Definitions and Units. Electrolytic conductivity is often defined as the electrical conductance of a unit cube of solution as measured between opposite faces. It is expressed in the same units as electrical conductivity, i.e.. reciprocal ohms per unit length. Most commonly wc find Mho/eemimeter (fU cm"1). siemens/cenlimeter IS cm 1), and siemcns/meler (S cnT1) ... 

The coefficient of thermal conductivity also called specific heat of conductivity is the q uantity of heat in gram calories transmitted per second thru a plate of the material one cm cube, when the temp difference between the two sides of the plate is one degree C (Ref l )... 

Computer simulation is invariably conducted on a model system whose size is small on the thermodynamic scale one typically has in mind when one refers to phase diagrams. Any simulation-based study of phase behavior thus necessarily requires careful consideration of finite-size effects. The nature of these effects is significantly different according to whether one is concerned with behavior close to or remote from a critical point. The distinction reflects the relative sizes of the linear dimension L of the system—the edge of the simulation cube, and the correlation length —the distance over which the local configurational variables are correlated. By noncritical we mean a system for which L E, by critical we mean one for which L [Pg.46]

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