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Entropy, temperature coefficient

We have already observed that the entropy theory of elasticity predicts a modulus of the right magnitude and possessing the proper temperature coefficient. Now let us examine the suitability of Eq. (3.39) to describe experimental results in detail. [Pg.150]

The acid hydrolysis of diaziridines has been investigated kinetic-ally. The reaction is first order and shows a relatively high temperature coefficient. Thus one finds a relatively high activation enthalpy (23-28 kcal) and a positive activation entropy (2-6 eu). The influence of substitution on nitrogen is small. The velocity of the diaziridine hydrolysis depends only in the weakly acid region on the acid concentration. Between pH 7 and 3 the fc-values rise by nearly 10 . For the... [Pg.120]

For all common substances the temperature coefficient of t is negative that is to say, the temperature coefficient of 1/e is positive hence (11) represents a loss of entropy on subjecting the homogeneous dielectric to the field. [Pg.14]

In any process the change in entropy is, of course, equal to the temperature coefficient of the change in free energy, taken with opposite sign ... [Pg.101]

Note 4. The Number of Dipoles per Unit Volume (Sec. 98). Between 25 and 100°C the value of 1 /t for water rises from TV to , while the increment in the value of l/(t — 1) is nearly the same, namely, from rs to TfV- Similarly in any solvent whose dielectric constant is large compared with unity the temperature coefficients of l/(e — 1) and of 1/e are nearly equal. In comparing the behavior of different solvents, let us consider now how the loss of entropy in an applied field will depend upon n, the number of dipoles per unit volume. Let us ask what will be the behavior if (e — 1) is nearly proportional to n/T as it is in the case of a polar gas. In this case we have l/(e — 1) nearly proportional to T/n and since in a liquid n is almost independent of T, wc have... [Pg.265]

The temperature coefficient of the potential of zero charge has often been suggested to indicate the orientation of solvent molecules at the met-al/solution interface. However, this view is based only on the response of a simple two-state model for the interfacial solvent, and on neglecting any contribution from the electronic entropy.76,77 This is in fact not the case. The temperature coefficient of 0in many instances is negative and of the... [Pg.23]

The Hg/dimethyl formamide (DMF) interface has been studied by capacitance measurements10,120,294,301,310 in the presence of various tetraalkylammonium and alkali metal perchlorates in the range of temperatures -15 to 40°C. The specific adsorption of (C2H5)4NC104 was found to be negligible.108,109 The properties of the inner layer were analyzed on the basis of a three-state model. The temperature coefficient of the inner-layer potential drop has been found to be negative at Easo, with a minimum at -5.5 fiC cm-2. Thus the entropy of formation of the interface has a maximum at this charge. These data cannot be described... [Pg.60]

The entropy of formation of the interface was calculated from the temperature coefficient of the interfacial tension.304 The entropy of formation has been found to increase with the nature of the electrolyte in the same sequence as the single cation entropy in DMSO.108, 09,329 The entropy of formation showed a maximum at negative charges. The difference in AS between the maximum and the value at ff=ocan be taken as a measure of the specific ordering of the solvent at the electrode/solution interface. Data 108,109304314 have shown that A(AS) decreases in the sequence NMF > DMSO > DMF > H90 > PC > MeOH. [Pg.61]

The semiconducting properties of the compounds of the SbSI type (see Table XXVIII) were predicted by Mooser and Pearson in 1958 228). They were first confirmed for SbSI, for which photoconductivity was found in 1960 243). The breakthrough was the observation of fer-roelectricity in this material 117) and other SbSI type compounds 244 see Table XXIX), in addition to phase transitions 184), nonlinear optical behavior 156), piezoelectric behavior 44), and electromechanical 183) and other properties. These photoconductors exhibit abnormally large temperature-coefficients for their band gaps they are strongly piezoelectric. Some are ferroelectric (see Table XXIX). They have anomalous electrooptic and optomechanical properties, namely, elongation or contraction under illumination. As already mentioned, these fields cannot be treated in any detail in this review for those interested in ferroelectricity, review articles 224, 352) are mentioned. The heat capacity of SbSI has been measured from - 180 to -l- 40°C and, from these data, the excess entropy of the ferro-paraelectric transition... [Pg.410]

The chemical potential difference —ju may be resolved into its heat and entropy components in either of two ways the partial molar heat of dilution may be measured directly by calorimetric methods and the entropy of dilution calculated from the relationship A i = (AHi —AFi)/T where AFi=/xi —/x or the temperature coefficient of the activity (hence the temperature coefficient of the chemical potential) may be determined, and from it the heat and entropy of dilution can be calculated using the standard relationships... [Pg.516]

Fig. 113.—Comparison of observed entropies of dilution (points and solid lines with results calculated for ASi according to Eq. (28) (broken line). Data for polydimethyl-siloxane, M =3850, in benzene, A (Newing ), obtained from measured activities and calorimetric heats of dilution. Entropies for polystyrene (Bawn et in methyl ethyl ketone,, and in toluene, O, were calculated from the temperature coefficient of the activity. The smoothed results for benzene solutions of rubber, represented by the solid curve without points, were obtained similarly. Fig. 113.—Comparison of observed entropies of dilution (points and solid lines with results calculated for ASi according to Eq. (28) (broken line). Data for polydimethyl-siloxane, M =3850, in benzene, A (Newing ), obtained from measured activities and calorimetric heats of dilution. Entropies for polystyrene (Bawn et in methyl ethyl ketone,, and in toluene, O, were calculated from the temperature coefficient of the activity. The smoothed results for benzene solutions of rubber, represented by the solid curve without points, were obtained similarly.
If we now calculate Cm from Eq. (7), the results of the foregoing analysis yield numerical values for the entropy of dilution parameters ypi in the various solvents. From the 0 s obtained simultaneously, the heat of dilution parameter Ki — 0 pi/T may be computed. To recapitulate, the value of in conjunction with gives at once Cm i(1--0/T). Acceptance of the value of Cm given by Eq. (7) as numerically correct makes possible the evaluation of the total thermodynamic interaction i(l —0/7"), which is equal to ( i—/ci). If the temperature coefficient is known, this quantity may be resolved into its entropy and energy components. [Pg.625]

The Gibbs-Helmholtz equation also links the temperature coefficient of Galvani potential for individual electrodes to energy effects or entropy changes of the electrode reactions occurring at these electrodes. However, since these parameters cannot be determined experimentally for an isolated electrode reaction (this is possible only for the full current-producing reaction), this equation cannot be used to calculate this temperature coefficient. [Pg.51]

Finally, we turn from solutions to the bulk state of amorphous polymers, specifically the thermoelastic properties of the rubbery state. The contrasting behavior of rubber, as compared with other solids, such as the temperature decrease upon adiabatic extension, the contraction upon heating under load, and the positive temperature coefficient of stress under constant elongation, had been observed in the nineteenth century by Gough and Joule. The latter was able to interpret these experiments in terms of the second law of thermodynamics, which revealed the connection between the different phenomena observed. One could conclude the primary effect to be a reduction of entropy... [Pg.50]

It can be shown that the usual relationships between temperature coefficients of the Gibbs function and entropy or enthalpy, respectively, also apply if stated for excess functions. Thus,... [Pg.374]

The model parameters are varied systematically within reasonable limits to fit the experimental results. The minimum positions of the rotational bond angles probably do not deviate more than 5° from planar trans and from symetrically staggered gauche, respectively. Entropy contributions to the free energies of the rotational isomers are discussed with respect to the influence on the temperature coefficient. [Pg.158]

The inter- and Intramolecular contributions to the entropy and energy of fusion are calculated for several linear aliphatic polyesters and polyamides assuming the fusion process consists of two Independent contributions the volume expansion (intermolecular contribution) and the increase in the conformational freedom of each polymer chain on melting (intramolecular contribution). The intramolecular entropy and energy contributions are obtained from the configurational partition function and Its temperature coefficient calculated for an isolated, unperturbed polymer chain using the RIS approximation. [Pg.257]

These expressions demonstrate that the change of entropy and internal energy on deformation under these conditions is both intra- and intermolecular in origin. Intramolecular (conformational) changes, which are independent of deformation, are characterized by the temperature coefficient of the unperturbed dimensions of chains d In intermolecular changes are characterized by the thermal expansivity a and are strongly dependent on deformation. The difference between the thermodynamic values under P, T = const, and V, T = const, is vefy important at small deformations since at X - 1 2aT/(/,2 + X — 2) tends to infinity. [Pg.42]

Cell emf values may therefore have positive or negative temperature coefficients, depending on the sign of the entropy change associated with the cell reaction. It should be noted that unless gases are involved in the latter, the entropy change and hence the temperature coefficient of the emf is usually very small. A useful practical form for the temperature dependence is... [Pg.33]

Issue is taken here, not with the mathematical treatment of the Debye-Hiickel model but rather with the underlying assumptions on which it is based. Friedman (58) has been concerned with extending the primitive model of electrolytes, and recently Wu and Friedman (159) have shown that not only are there theoretical objections to the Debye-Hiickel theory, but present experimental evidence also points to shortcomings in the theory. Thus, Wu and Friedman emphasize that since the dielectric constant and relative temperature coefficient of the dielectric constant differ by only 0.4 and 0.8% respectively for D O and H20, the thermodynamic results based on the Debye-Hiickel theory should be similar for salt solutions in these two solvents. Experimentally, the excess entropies in D >0 are far greater than in ordinary water and indeed are approximately linearly proportional to the aquamolality of the salts. In this connection, see also Ref. 129. [Pg.108]

Determination of both the energy (or enthalpy) of activation and the entropy of activation involves measurement of the temperature coefficient of the rate constant. The most usual procedure is to plot log k against I/T for a series of temperatures and to establish the best straight line. The slope is equal to — EJ2.303 R. With Ea established, one can obtain A8 for reactions in solution from equation (10)... [Pg.7]

The determination of standard transformed enthalpies of biochemical reactions at specified pH, either from temperature coefficients of apparent equilibrium constants or by calorimetric measurements, makes it possible to calculate the corresponding standard transformed entropy of reaction using... [Pg.174]

Temperature dependence and activation energy. The importance of the evaluation of the temperature coefficient of the reaction rate has been previously discussed (27). Since the oxidation rate follows a parabolic equation, it is possible to evaluate the rate constants and, using these constants, the energy and entropy of activation of the rate-controlling processes. [Pg.159]

The integral change in entropy, AS, is determined from the temperature coefficient of AG. The change in differential entropy of the adsorbent, AS, can be determined either from the difference between the changes in entropy of the integral... [Pg.363]

Entropy Change. The entropy change in the adsorption of water on barium sulfate is shown in Figure 8. The integral entropy, AS, calculated from AG and A ffl decreases monotonically with increasing amount adsorbed. AS can also be calculated from the temperature coefficient of v by... [Pg.370]

O Results calculated from temperature coefficient of x AHit. Change m partial molal entropy of barium sulfate... [Pg.371]

The change of the cell voltage as a function of the cell temperature (temperature coefficient) dEf fdT = -0.83xl0-4 VK 1 and the relationship between the standard reaction entropy and the standard free enthalpy of reaction (3AG /3T)p = -AS the value for the cell reaction can be calculated as -AS = -16.02 J K-1 mol-1. Refs. [i] Bockris JO M, Reddy AKN, Gamboa-Aldeco M (2000) Modern electrochemistry, vol 2A. Kluwer, Dordrecht, p 1356 [ii] Holze R (1989) Leitfaden der Elektrochemie. Teubner, Stuttgart [iii] Handel S (1971) A dictionary of electronics. Penguin Books, London [iv] Rieger PH (1994) Electrochemistry. Chapman-Hall, New York, p 2... [Pg.136]


See other pages where Entropy, temperature coefficient is mentioned: [Pg.201]    [Pg.141]    [Pg.51]    [Pg.73]    [Pg.446]    [Pg.186]    [Pg.42]    [Pg.17]    [Pg.356]    [Pg.68]    [Pg.911]    [Pg.145]    [Pg.175]    [Pg.174]    [Pg.197]    [Pg.326]    [Pg.148]    [Pg.149]    [Pg.363]    [Pg.372]    [Pg.539]    [Pg.169]   
See also in sourсe #XX -- [ Pg.49 ]




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