V. To arrange a number of voltaic cells to furnish a maximum current against a known external resistance. Let the electromotive force of each cell be E, and its internal resistance r. Let R be the external resistance, n the total number of cells. Assume that x cells are arranged in series and njx in parallel. The electromotive force of the battery is xE. Its internal resistance x2r/n. The current C, according to the text-books on electricity, is given by the relation [Pg.164]

Equation (6.308) implies that the isotropic diffusive motion along the coordinate axes is independent. Here, W/KT is the drift due to an external potential force field V, while V

Johannes van der Waals developed his famous equation of state by the introduction of both the attractive and the repulsive forces between the molecules. First he postulated that the gas behaves as if there is an additional internal pressure to augment the external applied pressure, which is based on the mutual attraction of molecules since the density of molecules is proportional to 1/V, the intensity of the binary attractive force would be proportional to 1/V. Then he postulated that when the measured total volume begins to approach the volume occupied by the real gaseous molecules, the free volume is obtained by subtracting the molecular volume from the measured volume. Then he introduced the parameter a, which represents an attractive force responsible for the internal pressure, and the parameter b, which represents the volume taken by the molecules. He arrived at [Pg.128]

The system of our choice will usually prevail in a certain macroscopic state, which is not under the influence of external forces. In equilibrium, the state can be characterized by state properties such as pressure (P) and temperature (T), which are called "intensive properties." Equally, the state can be characterized by extensive properties such as volume (V), internal energy (U), enthalpy (H), entropy (S), Gibbs energy (G), and Helmholtz energy (A). [Pg.7]

For each balance law, the values of -0, J and 4> defines the transported quantity, the diffusion flux and the source term, respectively, v denotes the velocity vector, T the total stress tensor, gc the net external body force per unit of mass, e the internal energy per unit of mass, q the heat flux, s the entropy per unit mass, h the enthalpy per unit mass, u>s the mass fraction of species s, and T the temperature. [Pg.91]

Here, v is the velocity vector field, p is the mass density of the fluid, D/Dt = S/Sf + V V is the material derivative, Vp is the gradient of the pressure, r[j is the shear viscosity, and F is the external force acting on the fluid volume. The right-hand side of Eq. (1) is a momentum balance between the internal pressure and viscous stress and the external forces on the fluid body. Any excess momentum contributes to the material acceleration of the fluid volume, on the left-hand side. [Pg.63]

In many cases of transport in solids, the atoms (ions) of one sublattice of the crystal are (almost) immobile. Here, we can identify the crystal lattice with the external (laboratory) frame and define the fluxes relative, to this immobile sublattice (to = 0). v° is bk-Xk (Eqn. (4.51)) where Xk is the sum of all local forces which can be applied externally (eg., an electric field), or which may stem from fields induced by the, (Fickian) diffusion process itself (eg., self-stresses). An example of such a diffusion process that leads to internal forces is the chemical interdiffusion of A-B. If the lattice parameter of the solid solution changes noticeably with concentration, an elastic stress field builds up and acts upon the diffusing particles, it depends not only on the concentration distribution, but on the geometry of the bounding crystal surfaces as well. [Pg.71]

General physical laws often state that quantities like mass, energy, and momentum are conserved. In computational mechanics, the most important of these balance laws pertains to linear momentum (when reckoned per unit volume, linear momentum may be expressed as the material density p times velocity v). The balance equation for linear momentum may be considered as a generalization of Newton s second law, which states that mass times acceleration equals total force. As we saw in the previous section, stresses in a material produce tractions, which may be considered as internal forces. In addition, external forces such as gravity may contribute to the total force. These are commonly reckoned per unit mass and are usually referred to as body forces to distinguish them from tractions, which may be considered as surface forces. For a one-dimensional motion, balance of linear momentum requires that (37,38) [Pg.431]

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