Clausius* postulate

We consider two equivalent physical expressions of the second law, one based on Kelvin s principle and the other a generalization of Clausius postulate. 

In 1865, building on the work of Kelvin, Sadi Carnot, and others who studied the efficiency of heat engines, Rudolf Clausius postulated that the entropy change of a system undergoing an infinitesimal reversible process was the heat absorbed (absolute temperature T (in kelvins) of the system ... 

Around 1850, however, the German physicist Rudolf Clausius and the English physicist William Thomson (later Lord Kelvin) independently showed that the concept of energy conservation implied that the work capacity of heat included the actual conversion of heat into work. Clausius and Thomson each independently formulated the limits for energy conversion processes of the second law. In 1865, Clausius postulated the fundamental principle of the constant increase of entropy. 

The theory of Kelvin (1854), developed in the preceding, section, stands midway between these two hypotheses, in that it assumes the existence of potential differences at the junctions, playing the role postulated by Clausius, and also admits the production of electromotive forces in the interior of the homo-, geneous wires due to inequalities of temperature in the latter, these inequalities giving rise to the flow of heat which is regarded as essential in the theory of Kohlrausch. 

Irreversible processes correspond to the time evolution in which the past and the future play different roles. In processes such as heat conduction, diffusion, and chemical reaction there is an arrow of time. As we have seen, the second law postulates the existence of entropy 5, whose time change can be written as a sum of two parts One is the flow of entropy deS and the other is the entropy production dtS, what Clausius called uncompensated heat, ... 

Kinetic theory of gases was given by Kronig, Clausius, Maxwell etc. to explain the behaviour of gases theoretically. This theory is applicable only to a perfect or an ideal gas. The main postulates or assumptions of the kinetic theory are ... 

In the previous section it was observed that the Langmuir postulates of sites of equal activity and no interaction between occupied and bare sites were responsible for nonagreement with experimental data. It might be surmised that these assumptions correspond to a constant heat of -ad-sm-pt-ion—Indeed.-it-is-p.QssibIe to derive the Langmuir isotherm by assuming that is independent of d. The heat of adsorption can be evaluated from adsorption-equilibrium data. First the Clausius-Clapeyron equation is applied to the two-phase system of gas and adsorbed component on the surface ... 

How intuitive is the statement How accustomed are students to the properties and phenomena involved in the statement How directly does the statement suggest the evidence for and consequences of the law Here is where most statements of the second law fall far short of what is desired. Consider Caratheodory1s, "In the neighborhood of any prescribed initial state, there jre states which cannot be reached by an adiabatic process." Is this really a good way to express what is one of the most profound and fruitful generalizations in all of science Again, the popular impossibility statements of Kelvin and of Clausius seem to be relatively minor truths, fine perhaps as corollaries, but intuitively not very obvious. The postulates... 

Proof II. In this proof we start from a physical postulate which embodies Clausius statement of the second law. The physical postulate is A... 

We annotate that Clausius states about the total entropy of the world. If the world consists of thermodynamic subsystems, each containing some entropy, then his statement concerns the total entropy, which is the sum of the entropies of the subsystems. In order to get the total entropy to a maximum, it is postulated that the subsystems cannot be made thermally insulated. In other words, the formulation of Clausius denies the existence of thermal nonconductive materials. 

The second part of the statement of Clausius suggests that the entropy of the world tends to become a maximum. This statement is often accepted as such, as a postulate. However, we may ask still more into depth if the entropy tends to a maximum, then a maximum should exist at all. 

The free-volume concept dates back to the Clausius [1880] equation of state. The need for postulating the presence of occupied and free space in a material has been imposed by the fluid behavior. Only recently has positron annihilation lifetime spectroscopy (PALS see Chapters 10 to 12) provided direct evidence of free-volume presence. Chapter 6 traces the evolution of equations of state up to derivation of the configurational hole-cell theory [Simha and Somcynsky, 1969 Somcynsky and Simha, 1971], in which the lattice hole fraction, h, a measure of the free-volume content, is given explicitly. Extracted from the pressure-volume-temperature PVT) data, the dependence, h = h T, P), has been used successfully for the interpretation of a plethora of physical phenomena under thermodynamic equilibria as well as in nonequilibrium dynamic systems. 

One of the difficulties in understanding the true mechanism of the process of electrolysis at the time that Faraday enunciated his laws of electrolysis was the absence of the idea of spontaneous electrolytic dissociation, postulated much later by Clausius and by Arrhenius. In fact, Faraday believed that the electric force at (between) electrodes split up molecules in the electrolyte, giving rise to conductivity. This idea was connected with Freiherr von Grotthus s theory of a series of dissociations and recombinations of charged species in the conductance of aqueous solutions. 

In the early 19th century (1803), Dalton proposed his atomic theory. In 1811, Amedeo Avogadro made clear the distinction between atoms and molecules of elementary substances, hi addition, the concepts of heat, energy, work, and temperature were developed. The first law of thermodynamics was set forth by Julius Robert von Mayer and the second law of thermodynamics was postulated by Rudolf Julius Emanuel Clausius and William Thomson (Lord Kelvin). Later in the century, Clausius, Ludwig Boltzmarm, and James Clerk Maxwell related the ideal gas law in terms of a kinetic theory of matter. This led to the kinetics of reactions and the laws of chemical equilibrium. 

Now if the first term in brackets exceeds the second, dEA will necessarily increase i.e., heat will flow into A without external intervention, which requires, according to Clausius, that A will be colder than B. Thus, (din g/dE) is seen to be a measure of the hotness level of a system. To quote Waldram A larger value of (din g/dE) sucks energy into itself. Normally, g increases very rapidly with E. In fight of the above, it is then sensible to postulate the association... 

All of the above follows from the two equivalent postulates by Kelvin and Clausius. They constitute the second law of thermodynamics. However, mathematical... 

Clausius asserts that if there were some working substance, or engine, to provide more work for the fall of a given amount of heat than another engine or, what amounts to the same thing, were it to provide the same work for the fall of a smaller amount of heat, then if the first engine drives the second one in reverse we would have an entirely anomalous result no net work would be done and heat would, in effect, flow from a cold to a hot body. This, he postulates, is quite impossible and thus he proves Carnot s fondamental principle. 

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