The Establishment of Thermodynamics

We enter thus the 19th century that saw the establishment of thermodynamics through the development of the first and second laws. But first let us summarize the state of the Science of Heat and of the Steam Engine in the early part of the 19th century. 

Heat is made of fire particles (caloric), even though some disagree 

1842 Mayer publishes his theory about the conversion of heat 

1843-1850 Joule, through a series of experiments, establishes the convertibility of work to heat. 

1849 Kelvin expresses doubts that both Carnot and Joule can be right also introduces the term Thermodynamics. 

---

In equilibrium sampling, the exposure time is sufficiently long to permit the establishment of thermodynamic equilibrium between the water and sorption phases. In this case the dissolved analyte concentration can be estimated using the sorption phase-water partition coefficient (Ksw) ... 

Not only does the melting process depend on the thermal history of the sample, the isotropization of the polymeric nematic phase is also history-dependent. Feijoo and coworkers (1988 1990) are apparently the first to have studied in detail the effect on the isotropization of the thermal treatment. According to these researchers the establishment of thermodynamic equilibrium in the nematic phase was not as quick as has been commonly believed, for both the nematic and the isotropic phases are fluid states. They found that the heat and temperature of isotropization of the polymeric nematic phase were remarkably affected by the preceding... 

As we saw in the preceding chapter, one of the characteristics of the biochemical machine is a constant opposition to the establishment of thermodynamic equilibrium. 

To produce a C02-enriched liquid one can add CO2 to the autoclave. The CO2 then dissolves into the liquid until the thermodynamic equilibrium is reached. The amount of CO2 that at most can be dissolved in the liquid depends on the liquid itself and on the temperature and the pressure as exemplary shown in Fig. 7.2. To accelerate the establishment of thermodynamic equilibrium the autoclave can be shaken. For the experiments, this is done for 1 h. After that, the autoclave is set in an upright position for at least 2 h. Hence, undissolved gas bubbles can ascend toward the interphase. The gas-saturated liquid then is homogenous and forms a single phase. 

We assume that the unbinding reaction takes place on a time scale long ( ompared to the relaxation times of all other degrees of freedom of the system, so that the friction coefficient can be considered independent of time. This condition is difficult to satisfy on the time scales achievable in MD simulations. It is, however, the most favorable case for the reconstruction of energy landscapes without the assumption of thermodynamic reversibility, which is central in the majority of established methods for calculating free energies from simulations (McCammon and Harvey, 1987 Elber, 1996) (for applications and discussion of free energy calculation methods see also the chapters by Helms and McCammon, Hermans et al., and Mark et al. in this volume). 

This event marked the turning point in Joule s career. From 1847 on, when Joule spoke, scientists listened. His research results were one of the two major contributions to the establishment of the first law of thermodynamics, the other being that of the... 

If Comte had lived long enough to see the development of thermodynamics and its applications, he might have retracted these words. However, he died well before the work of Black, Rumford, Hess, Carnot, Joule, Clausius, Kelvin, Helmholtz, and Nernst that established different aspects of the sciences, followed by the contributions of Gibbs, Lewis, and Guggenheim that unified the science into a coherent whole.a... 

Although liquid Hg would never be used as a reference (model) surface in surface physics because its liquid state and high vapor pressure do not allow appropriate UHV conditions, this metal turns out to be a reference surface in electrochemistry for precisely the same reasons reproducibility of the surface state, easy cleaning of its surface, and the possibility of measuring the surface tension (surface thermodynamic conditions). In particular, the establishment of a UHV scale for potentials is at present based on data obtained for Hg. 

Figure 6.3 shows a free energy profile for a reaction in which B is thermodynamically more stable than C (lower AG), but C is formed faster (lower AG ). If neither reaction is reversible, C will be formed in larger amount because it is formed faster. The product is said to be kinetically controlled. However, if the reactions are reversible, this will not necessarily be the case. If such a process is stopped well before the equilibrium has been established, the reaction will be kinetically controlled since more of the faster-formed product will be present. However, if the reaction is permitted to approach equilibrium, the predominant or even exclusive product will be B. Under these conditions, the C that is first formed reverts to A, while the more stable B does so much less. We say the product is thermodynamically controlled.Of course. Figure 6.3 does not describe all reactions in which a Compound A can give two different products. In many cases, the more stable product is also the one that is formed faster. In such cases the product of kinetic control is also the product of thermodynamic control. 

To illustrate this, we shall start with 2500 A ingredients and set the transition probabilities to Pi (A B) = 0.01, Pi (B A) = 0.02, Pi (A C) = 0.001, and Pi (C A) = 0.0005. Note that these values yield a situation favoring rapid initial transition to species B, since the transition probability for A B is 10 times than that for A C. However, the formal equilibrium constant eq[C]/[A] is 2.0, whereas eq[B]/[A] = 0.5, so that eventually, after the establishment of equilibrium, product C should predominate over product B. This study illustrates the contrast between the short run (kinetic) and the long run (thermodynamic) aspects of a reaction. To see the results, plot the evolution of the numbers of A, B, and C cells against time for a 10,000 iteration run. Determine the average concentrations [A]avg, [B]avg, and [C]avg under equilibrium conditions, along with their standard deviations. Also, determine the iteration Bmax at which ingredient B reaches its maximum value. 

Before treating specific faradaic electroanalytical techniques in detail, we shall consider the theory of electrolysis more generally and along two different lines, viz., (a) a pragmatic, quasi-static treatment, based on the establishment of reversible electrode processes, which thermodynamically find expression in the Nernst equation, and (b) a kinetic, more dynamic treatment, starting from passage of a current, so that both reversible and non-reversible processes are taken into account. 

This permits provisional calculation of the compositional dependence of the equilibrium constant and determination of provisional values of the solid phase activity coefficients (discussed below). The equilibrium constant and activity coefficients are termed provisional because it is not possible to determine if stoichiometric saturation has been established without independent knowledge of the compositional dependence of the equilibrium constant, such as would be provided from independent thermodynamic measurements. Using the provisional activity coefficient data we may compare the observed solid solution-aqueous solution compositions with those calculated at equilibrium. Agreement between the calculated and observed values confirms, within the experimental data uncertainties, the establishment of equilibrium. The true solid solution thermodynamic properties are then defined to be equal to the provisional values. 

The pursuit of chemical thermodynamics, especially its applications in solution chemistry and electrochemistry, resulted in the establishment of a distinct scientific discipline of physical chemistry by the so-called Ionists in the late nineteenth century. These practitioners defined their aim as "theoretical chemistry," bridging the domains of physics and chemistry. Ostwald contrasted the aims and methods of the new discipline with the practices of organic chemists, whom he characterized as powerful, hidebound, fact-mongering opponents of the young band of Ionists. 

The first chair of theoretical physics in France was the professorship established for Pierre Duhem in 1894 at the Bordeaux Faculty of Sciences. 1 Duhem was well known in French scientific circles not only as a physicist but as a physicist of exceptional mathematical skills who addressed himself early in his scientific studies to chemical problems. He wrote a controversial doctoral thesis (1886) in which he developed the concept of thermodynamic potential for chemistry and physics, and he later developed a treatment of equilibrium processes formally analogous to the mechanics of Lagrange. The goal was to make mechanics a branch of the more general science of thermodynamics, a science that embraces "every change of qualities, properties, physical state, chemical constitution. "2... 

The action of added ion-pairs may also be visualized as the establishment of an ion-pair atmosphere about a dipolar transition state. Simple thermodynamic treatment predicts linearity of log k3 in cs, but it has been shown that contributions of ion-pair-ion-pair repulsion, higher aggregation, and the effect of salt on the dielectric constant introduce curvature in the log k3-cs plot that is in the direction of a k3-cs dependence. 

A reversible equilibrium can usually be detected in either of two ways (a) In the transition region, the attainment of a time-independent value of the physical observable implies the establishment of a reversible equilibrium. (b) The reversal of solution conditions will lead to a reversal in the value of the physical observable if the transition under study is under thermodynamic control. The observable may be the optical density of the solution, and the solution conditions may be determined by temperature and pressure. An irreversible change is encountered if the physical observable cannot attain a time-independent value in the transition region, nor be reversed by reversal of the solution conditions (Brandts et al., 1970). 

---