Voltage temperature coefficient

The temperature voltage coefficient has several names temperature coefficient, voltage coefficient or temperature coefficient of voltage. Table 7.3 contains a few values of (d (emf)/dT). 

Worked Example 7.7 The temperature voltage coefficient for a simple alkaline torch battery is —6.0 x 10 4 VK-1. What is the entropy change associated with battery discharge The number of electrons transferred in the cell reaction n = 2. 

Figure 7.5 Graph of cell emf against temperature for the Clark cell Hg HgS04, ZnS04(sat d) Zn. We call the gradient of this graph the temperature voltage coefficient ...

Table 7.3 Temperature voltage coefficients for various cells and half cells...

SAQ 7.6 The emf of a lithium watch battery is exactly 3.000 V at 298 K, but the value decreases to 2.985 V at 270 K. Calculate the temperature voltage coefficient and hence the change in entropy AS(ceii) during cell discharge. (Take n = 1.)... 

Occasionally, the temperature voltage coefficient is not expressed as a simple number, but as apower series in T (we generally call it a virial series, or expansion). For example, Equation (7.19) cites such a series for the cell Pt(S) H2(g) HBr(aq) AgBr(s) Ag(s) ... 

Stability The SSCE has the smallest temperature voltage coefficient of any common reference electrode... 

Figure 18.24 Comparison of the magnetoelectric effect in granular and laminated composites, (a) maximum ME voltage coefficient of the PZT and Ni-ferrite particulate composites as functions of sintering temperature and Ni-ferrite particle content ...

With and 7 2 being the reverse currents of D and D2. and 2 the emission coefficients and Uj- is the temperature voltage. For very small voltages follows ... 

Ideally a standard cell is constmcted simply and is characterized by a high constancy of emf, a low temperature coefficient of emf, and an emf close to one volt. The Weston cell, which uses a standard cadmium sulfate electrolyte and electrodes of cadmium amalgam and a paste of mercury and mercurous sulfate, essentially meets these conditions. The voltage of the cell is 1.0183 V at 20°C. The a-c Josephson effect, which relates the frequency of a superconducting oscillator to the potential difference between two superconducting components, is used by NIST to maintain the unit of emf. The definition of the volt, however, remains as the Q/A derivation described. 

The primary thermoelectric phenomena considered in practical devices are the reversible Seebeck, Peltier, and, to a lesser extent, Thomson effects, and the irreversible Eourier conduction and Joule heating. The Seebeck effect causes a voltage to appear between the ends of a conductor in a temperature gradient. The Seebeck coefficient, L, is given by... 

Voltage measurement have been made at very low temperatures using a superconductor as one leg of a thermocouple. Eor a superconductor, S is zero, so the output of the couple is entirely from the active leg. The Thomson heat is then measured at higher temperatures to extend the absolute values of the Seebeck coefficients (7,8). The Thomson heat is generally an order of magnitude less than the Peltier heat and is often neglected in device design calculations. 

The temperature dependence of the open circuit voltage has been accurately determined (22) from heat capacity measurements (23). The temperature coefficients are given in Table 2. The accuracy of these temperature coefficients does not depend on the accuracy of the open circuit voltages at 25°C shown in Table 1. Using the data in Tables 1 and 2, the open circuit voltage can be calculated from 0 to 60°C at concentrations of sulfuric acid from 0.1 to 13.877 m. 

The temperature dependence of the equilibrium cell voltage forms the basis for determining the thermodynamic variables AG, A//, and AS. The values of the equilibrium cell voltage A%, and the temperature coefficient dA< 00/d7 which are necessary for the calculation, can be measured exactly in experiments. 

Figure 13. Voltage relaxation method for the determination of the diffusion coefficients (mobilities) of electrons and holes in solid electrolytes. The various possibilities for calculating the diffusion coefficients and from the behavior over short (t L2 /De ) and long (/ L2 /Dc ll ) times are indicated cc h is the concentration of the electrons and holes respectively, q is the elementary charge, k is the Boltzmann constant and T is the absolute temperature.

These relationships can be used to obtain thermodynamic data otherwise difficult to get. Vice versa they can be used to calculate the temperature coefficient of a cell voltage respectively an electrode potential based on known thermodynamic data. 

Battery characteristics depend strongly on the operating temperature. As a rule, both the discharge voltage and the reactant utilization coefficient are lower at lower temperatures. On the other hand, increased temperatures are conducive to side reactions (such as corrosion processes) and thus reduce battery efficiency. Therefore, each battery type is designed for a specific temperature range within which its characteristics will be within the prescribed limits. 

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