Difference of Potential

Contact Difference of Potential.—Suppose we have two metals, a and 6, in the same container at the same temperature. For each one, we can calculate the vapor pressure of the electron gas in equilibrium with it by Eq. (2.2). Since this equation depends on the properties of the metal, we shall get a different answer in the two cases. That is, an electron gas in equilibrium with one metal, say one with a low work function, will have too great a pressure to be in equilibrium with the second metal with a larger work function. Let us use a kinetic argument to see what will happen and what sort of final equilibrium we may expect. Suppose the metal a, of low work function, has established its equilibrium pressure in the electron gas, and then the metal b is introduced into the container and brought to the same temperature. The gas pressure is too great for equilibrium with b, so that more electrons will strike its surface and 

Let us now investigate the Volta effect more quantitatively. When equilibrium is established, there will be a difference of potential between the empty space outside the two metals. The potential energy of an electron in this space will then be as in Fig. XXVIII-2. The jump in potential at the surface of each metal is as in Fig. XXVIII-1, but now the potential varies from one metal to another. Since metal b is negatively charged, the potential in its neighborhood is less than near metal a, and the potential energy of an electron, which is — e times the electrostatic potential, will be greater. The difference of potential between empty 

The electrons in the empty space now form a perfect gas in an external force field. This problem has been discussed in Section 4, Chap. IV. There we found that in such a case the temperature of the gas is constant throughout, but the pressure and the density vary from point to point, the 

It is now clear what conditions we must have for equilibrium between metal a, metal 6, and the gas. The vapor pressure outside metal a must be the correct one for thermal equilibrium with that metal, the pressure outside b must be the correct one for equilibrium with it, and the pressures outside the two metals must be related according to the Boltzmann factor, to ensure equilibrium between the different parts of the gas. Thus let the potential energy of a mole of electrons outside the metal a bo Eaf and outside metal b be E. Then the Boltzmann factor leads to the relation 

Equation (4.2) is the condition of equilibrium of the gas. At the same time, we must have the gas in equilibrium with each metal, which means that Pa and Pb must be given by Eq. (2.1). Thus we have 

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The unit of electrical potential is the volt (V) which is the difference of potential between two points of a conducting wire which carries a constant... 

The unit of electrical resistance is the ohm (Q) which is the resistance between two points of a conductor when a constant difference of potential of one volt applied between these two points produces a current of one ampere. 

If an electrolyte AB is distributed between two solvents, a and f3, there will in general be a difference of potential established across the boundary, due to the existence of a double layer ( 198). 

In the above we have assumed that no other forces than the electrical are acting at the surface of separation. In general, there will be the capillary forces as well, and we have to take account of the influence of the electrical double layer in considering the adsorption of an electrolyte. If w is the area of the surface, o the interfacial tension, e the charge per unit area, and E the difference of potential, we shall have ... 

If a bar of zinc is dipped into a solution of zinc sulphate, the former acquires a negative, the latter a positive charge, and a difference of potential is established at the boundary the magnitude of which depends on the concentration of the solution. There is in fact an electrical double layer produced, which is formed of negative charges on the metal (which has lost ions into the solution) ... 

E0 is the difference of potential in a solution of zinc ions of unit concentration. In practice it is more convenient to use the concentration than c ( 121), and since in dilute solutions the two are proportional, we can write ... 

Differences of Potentials of Zero Charge of Various Metals with Respect to Pb ... 

Thus, the integral of the field g along a path is expressed by the difference of potentials at terminal points of this path. Certainly, it is much simpler to take a difference of the scalar at these points U b)—U a), than to perform an integration, and this fact demonstrates another advantage of using the potential. 

The ends of a correctly constructed electrochemical circuit measuring electrical potential difference must always have metals or conductors with identical chemical composition. It is usually reached by simple connection of two metals by copper wires. The inclusion between two metal conductors of a third metal conductor according to Volta s law does not change the difference of potentials at the output of a circuit. The difference of potentials in an electrochemical circuit at equilibrium is caused by the change of Gibbs free energy during the appropriate electrochemical reaction ... 

If two zinc electrodes are set up in opposition to one another as in Figure 6.12 (A), the difference of potential between them, measured by a potentiometer or voltmeter, is zero. If an infinitesimally small external emf is applied to the electrodes so that A is positive and B is negative, a very small current flows round the circuit, and Zn atoms pass from A into solution as Zn2+ ions, and Zn2+ ions leave the solution and are deposited as Zn atoms on B. If the small emf is reversed so that B is positive and A is negative, the current flows in the opposite direction, and zinc is dissolved from B and deposited on A. An electrode such as the zinc electrode, which reacts thus to an infinitesimal applied emf, is known as a reversible electrode. The hydrogen electrode described earlier is a reversible electrode. If two molar hydrogen electrodes are set up in opposition to one another, Figure 6.12 (B), the... 

Again, the consideration of the electrical potential in the electrolyte, and especially the consideration of the difference of potential in electrolyte and electrode, involve the consideration of quantities of which we have no apparent means of physical measurement, while the difference of potential in pieces of metal of the same kind attached to the electrodes is exactly one of the things which we can and do measure. 

The short wave-length limit of the X-radiation produced by the above difference of potential of 11,890 volts was 1.040 A. The point to be decided by these experiments was how close to this particular wavelength limit the average, or effective wave-length of the beam of X-rays coming from the mercury vapor really lay. 

Since we are interested in controlling accurately the potential of the working electrode (in order to condition the rate of the electron transfer between this electrode and the electroactive species), we must work on the difference of potential between the two electrodes. It is clear, however, that changing the applied potential between the two electrodes causes unpredictable variations in the potential of either the working electrode, or the counter electrode, or in the iR drop. This implies that it... 

As deducible from Figure 8, to apply a precise potential value to the working electrode means to apply a precise difference of potential between the working and the reference electrodes. Since the electronic circuit to monitor such potential difference, V, is properly assembled to possess a high input resistance, only a small fraction of the current generated in the electrochemical cell as a consequence of the applied potential enters the reference electrode (thus not modifying its intrinsic potential) most current is channelled between the working and the auxiliary electrodes. 

When a difference of potential AE is applied to the two plates, an excess q of electrons accumulates on one of them (which is equal to the... 

AE = the difference of potential applied between the two plates (in volts),... 

In other words, when one applies a difference of potential between the two plates of a capacitor, a current flows through the circuit until the capacitor is charged this current is called the capacitive current. 

As a result of the difference of potential AE applied between the working and reference electrodes, a capacitive current generates inside the cell which flows as a function of time, according to the relation ... 

It is hence evident that if we would have applied a difference of potential AE between the reference and the working electrodes before the complexation, we would have generated a current due to the oxidation process, Figure 35a. In contrast, upon applying the same potential difference AE after the cation complexation, we do not produce current if we wish to generate current we have to apply an extra potential AE, Figure 35b. The extent of AE is intuitively correlated to the nature of the complexed cation. From here we get the term cationic sensor. 

From equation (3.4.31), if the ratio n/nso is unity there will be no net current flow across the interface this condition is depicted in Fig. 3.13(a) for an n-type semiconductor. Under this equilibrium state surface electrons can undergo isoenergetic electron transfers to the redox species due to a built-in potential, equal to the difference of potential between Ecb and Eredox- Equilibrium can be perturbed, with a resulting observable transient current flow, by varying the concentrations of the redox species. The surface electron concentration ng is related to the bulk concentration no by the potential difference of the space charge layer as follows ... 

If we imagine that if coulombs of electricity be transported across a boundary separating two solutions of a monovalent electrolyte MX of concentrations Ci and Cg, the electrical work performed will be V F, where Fg is the difference of potential between the two solutions. 

In the discussion on the liquid-liquid potentials it has been shown that the interposition of a layer of oil between two aqueous solutions of an electrolyte may give rise to a difference of potential between the two aqueous layers. Such cells may be reversible with respect to either ion, and may therefore be regarded as cells permeable to one ion. 

Whereas on the NOPHO ALL-92 protocol patients did not regularly receive cranial radiotherapy, 6-MP application concurrent with cranial irradation during early maintenance was lower on BFM compared to St. Jude protocols (50 vs. 75mg/m2/d). Other differences of potential importance to this issue, which only apply to the comparison of... 

The first approach (Section 8.2.4) at this computation ran along the following lines The electrical work of activation arises because in the activation process charges have to be moved through the difference of potential between the initial and activated states, i.e., from xl + x2 to xl in Fig. 8.17. It was necessary, therefore, to know what fraction of the total j ump distance is the distance between the initial state and the barrier peak. This distance ratio was defined as the symmetry factor P, i.e.,... 

Electrostatic Capacity. The ratio of quantity of static electricity to the difference of potential... 

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