Formulation of Clausius

Several famous scientists have contributed to certain aspects of the second law of thermodynamics, among them are Carnot, Joule, Kelvin, Clausius, Planck, and Boltzmann. Various formulations of the second law have been created. This process still continues. Subsequently we will mainly focus on the formulation of Clausius. 

The principle of maximum entropy is widespread in other disciplines besides thermodynamics, for example, in information theory, economics. In fact, it implies to maximize the probability of a state of a system under certain constraints [5], 

The formulation of the second law according to Clausius in the version from 1865 consists essentially of two statements. 

Rudolf Julius Emanuel Clausius, bom Jan. 2, 1822, in Kolin, died Aug. 24, 1888, in Bonn. 

Die Energie der Welt ist konstant. Die Entropie der Welt strebt einem Maximum zu. The 

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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. 

Other formulations of the second law have appeared in science. Some of these originate even earlier than the formulation of Clausius. 

In an obituaiy talk given at the Physical Society of Berlin in 1889, Hermann Helmholtz stressed that Clausius s strict formulation of the mechanical heat theory is one of the most surprising and interesting achievements of the old and new physics, because of the absolute generality independent of the nature of the physical body and since it establishes new, unforeseen relations between different branches of physics. 

If the system is not isolated, its entropy may either increase or decrease. Thus, if a mass of gas is compressed in a cylinder impervious to heat, its entropy increases, but if heat is allowed to pass out into a medium, the entropy of the gas may decrease. By including the"gas and medium in a larger isolated system, we can apply (10) of 45, and hence show Jhat the medium gains more entropy than the gas loses. An extended assimilation of this kind shows that, if every body affected in a change is taken into account, the entropy of the whole must increase by reason of irreversible changes occurring in it. This is evidently what Clausius (1854) had in mind in the formulation of his famous aphorism The entropy of the universe strives towards a maximum. The word universe is to be understood in the sense of an ultimately isolated system. 

The full significance of these observations could not be appreciated in advance of the formulation of the second law of thermodynamics by Lord Kelvin and Clausius in the early 1850 s. In a paper published in 1857 that was probably the first to treat the thermodynamics of elastic deformation, Kelvin showed that the quantity of heat Q absorbed during the (reversible) elastic deformation of any body is related in the following manner to the change with temperature in the work — TFei required to produce the deformation ... 

The term entropy, which literally means a change within, was first used in 1851 by Rudolf Clausius, one of the formulators of the second law of thermodynamics. A rigorous quantitative definition of entropy involves statistical and probability considerations. However, its nature can be illustrated qualitatively by three simple examples, each demonstrating one aspect of entropy. The key descriptors of entropy are randomness and disorder, manifested in different ways. 

The general inequality (4.48) leads to the famous Clausius formulation of the second law ... 

Boltzmann [3]. Boltzmann was led to thiB generalized formulation of the problem by some attempts he had undertaken (1866) 11] to derive from kinetic concepts the Camot-Clausius theorem about the limited convertibility of heat into work. In order to carry through such a derivation for an arbitrary thermal system (Boltzmann [5], (1871)) it was necessary to calculate, e.g., for a nonideal gas, bow in an infinitely slow change of the state of the system the added amount of heat is divided between the translational and internal kinetic energy and the various forms of potential energy of the gas molecule. It is just for this that the distribution law introduced above is needed. 

The above definitions reflect the Clausius view of the origin of entropy at the beginning of the twentieth century a reformulation of thermodynamics by -> Born and Caratheodory showed firstly that the formulation of the second law of - thermodynamics requires a consideration of the heat and work relationships of at least two bodies, as implicitly discussed above, and that entropy arises in this formulation from the search for an integrating factor for the overall change in heat, dq when the simultaneous changes in two bodies are considered. The Born-Caratheodory formulation then leads naturally to the restriction that only certain changes of state are possible under adiabatic conditions. 

Thermodynamics first emerged as a science after the construction and operation of steam engines in 1697 by Thomas Savery and in 1712 by Thomas Newcomen in England. Later, Carnot, Rankine, Clausius, Kelvin, Gibbs, and many others developed formulations of thermodynamic principles for describing the conservation and conversion of energy. 

The work of Carnot, published in 1824, and later the work of Clausius (1850) and Kelvin (1851), advanced the formulation of the properties of entropy and temperature and the second law. Clausius introduced the word entropy in 1865. The first law expresses the qualitative equivalence of heat and work as well as the conservation of energy. The second law is a qualitative statement on the accessibility of energy and the direction of progress of real processes. For example, the efficiency of a reversible engine is a function of temperature only, and efficiency cannot exceed unity. These statements are the results of the first and second laws, and can be used to define an absolute scale of temperature that is independent of ary material properties used to measure it. A quantitative description of the second law emerges by determining entropy and entropy production in irreversible processes. 

Clausius, Equilibrium and Change The equilibrium state of the system plus its surroundings is thus one in which S has attained a maximum value. The well-known Clausius formulation of this is Die Energie der Welt ist konstant die Entropie der Welt strebt einem maximum zu. While it would be possible to characterize equilibrium and disequilibrium of chemical systems in terms of these entropies, there are more convenient ways to operate in chemical thermodynamics by concentrating on changes in the system itself (Atkins, 1990). 

From the original statement of Clausius other formulations can be derived that are equivalent and more applicable to other practical issues. 

In simple words, this means that the total entropy cannot decrease by any process. This formulation is a somewhat more rigorous formulation of the second statement of Clausius concerning that the entropy tends to become a maximum. If this formulation states that a process associated with a decrease of entropy is not possible, it allows a process where the entropy does not increase, i.e a process where the entropy remains constant. Such a process is an idealized process. We should emphasize that in a real process in which the thermodynamic parameters are changing always an increase of entropy occurs, even when the process can be directed close to the ideal process where the entropy remains constant. Actually, a process where the entropy does not change plays an important role in theoretical consideration. 

This Statement was later refined by Planck. On first glance, the formulation of the second law of Clausius and the formulation of Kelvin and Planck do not seem to have much in common. However, it is shown in elementary texts that both formulations are equivalent. 

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