Thermodynamics Clausius statement

It was the principal genius of J. W. Gibbs (Sidebar 5.1) to recognize how the Clausius statement could be recast in a form that made reference only to the analytical properties of individual equilibrium states. The essence of the Clausius statement is that an isolated system, in evolving toward a state of thermodynamic equilibrium, undergoes a steady increase in the value of the entropy function. Gibbs recognized that, as a consequence of this increase, the entropy function in the eventual equilibrium state must have the character of a mathematical maximum. As a consequence, this extremal character of the entropy function makes possible an analytical characterization of the second law, expressible entirely in terms of state properties of the individual equilibrium state, without reference to cycles, processes, perpetual motion machines, and the like. 

Moreover, if is always positive and nonzero, W must be positive and nonzero except in the case when the two temperatures are equal. This observation results in the Clausius statement of the second law of thermodynamics Heat of itself will not flow from a heat reservoir at a lower temperature to one at a higher temperature. It is in no way possible for this to occur without the agency of some system operating as a heat engine in which work is done by the surroundings on the system. 

This T, the thermodynamic or absolute temperature, is here a function of S, V and x. But it s easy to show that if T were a function of temperature and entropy, or if it were a function of temperature and anything else, we could violate Kelvin s statement. So T depends only on the empirical temperature, and this dependence must be the same for all systems in order for the entropy of a composite to equal the sum of the entropies of the subsystem. In order for Clausius statement to hold in the case of irreversible processes, the equal sign of rfQ = TdS becomes <, and we have Clausius inequality TdS,rwKere T is the... 

The famous Clausius statement is as follows It is impossible to construct a device to work in a cyclic process whose sole effect is the transfer of heat from a body at a lower temperature to a body at a higher temperature. Clausius also stated the first and the second laws of thermodynamics combined together as The energy of the universe is constant, and The entropy of the universe tends toward a maximum. ... 

The second law of thermodynamics dictates that certain processes are irreversible. For example, heat travels in a direction of decreasing temperature. There are two commonly cited equivalent qualitative statements to the second law. The Kelvin-Planck statement states that it is impossible to construct any cyclic device that receives heat from a single thermal reservoir and converts it entirely into work. According to the Clausius statement, it is impossible to construct a device, which operates in a cycle that produces no other effect on the environment other than the transfer of heat from a low temperature reservoir to a higher temperature reservoir. Both of the Kelvin-Planck and Clausius statements of the second... 

The plan of the remaining sections of this chapter is as follows. In Sec. 4.3, a h)q)o-thetical device called a Carnot engine is introduced and used to prove that the two physical statements of the second law (the Clausius statement and the Kelvin-Planck statement) are equivalent, in the sense that if one is true, so is the other. An expression is also derived for the efficiency of a Carnol engine for Ihe purpose of defining thermodynamic temperature. Section 4.4 combines Carnot cycles and the Kelvin-Planck statement to derive the existence... 

There are several formulations of the second law of thermodynamics.The so-called Clausius statement says that in spontaneous processes heat cannot fiow from a lower-temperature body to a higher-temperature body. The Thomson (Lord Kelvin) statement says that heat cannot be completely converted into work. 

The second law of thermod5mamics is stated through the Kelvin-Planck statement and the Clausius statement. The Inequality of Clausius is a consequence of the second law of thermod5mamics, and it is stated for a system undergoing a thermodynamic cycle as... 

The Clausius statement is named for Rudolf Julius Emmanuel Clausius, 1822-1888, a German physicist who is generally considered to be the discoverer of the second law of thermodynamics. 

Kelvin s statement of the second law of thermodynamics is that heat put into a system that undergoes a cyclic process cannot be completely converted into work done on the surroundings. Clausius statement of this law is that heat cannot flow from a cooler to a hotter body if nothing else happens. The mathematical statement of the second law was shown to be a consequence of the Kelvin statement. It asserts that S, the entropy, is a state function if we define... 

Second Law of Thermodynamics. There have been numerous statements of the second law. To paraphrase Clausius It is impossible to devise an engine or process which, working in a cycle, will produce no effect other than the transfer of heat from a colder to a warmer body. According to Caratheodory, the Second Law can be stated as follows Arbitrarily close to any given state of any closed system, there exists an unlimited number of other states which it is impossible to reach from a given state as a result of any adiabatic process, whether reversible or not . 

Table 5.1 summarizes the various constraint conditions and the associated thermodynamic potentials and second-law statements for direction of spontaneous change or condition of equilibrium. All of these statements are equivalent to Carnot s theorem ( dq/T < 0) or to Clausius inequality ([Pg.164]

From the discussion of heat engines, the second law of thermodynamics states that it is impossible to achieve heat, taken from a reservoir, and convert it into work without simultaneous delivery of heat from the higher temperature to the lower temperature (Lord Kelvin). It also states that some work should be converted to heat in order to make heat flow from a lower to a higher temperature (Principle of Clausius). These statements acknowledge that the efficiency of heat engines could never be 100% and that heat flow from high temperatures to low temperatures is not totally spontaneous. Simply, the second law states that natural processes occur spontaneously toward the direction in which less available work can be used. 

Xt, , xn and is completely independent of the direction in time of the development of the natural processes.1 As a result, the fact of the reversibility of the mechanical motion, which is inescapable in the kinetic interpretation of the laws of thermodynamics, lost some of its importance. Nevertheless, even today many physicists are still following Clausius, and for them the second law of thermodynamics is still identical with the statement that the entropy can only increase.3... 

The first statement of the second law of thermodynamics was by Clausius,4 although early ideas came from Carnot5 in 1824. 

Clausius himself, later on, introduced the concept of entropy. Studies on entropy led to the evolution of the Third Law of Thermodynamics in 1906 by Nemst (1907). This was many times debated and revised till 1912, when Plank (1927) went back to practically the same statement as that of Nemst. 

There were some contradictions in Carnot s work—a result of his reliance on the caloric theory—that were subsequently cleared up by Clausius. Clausius accepted Carnot s proposition that some heat must be thrown away when converting heat to work as a law of nature, something that cannot be proved or derived from something else, but as far as we have ever been able to tell describes the way the world works. He called it the second law of thermodynamics and then sought to recast it in a different, more general, form that did not apply to heat engines alone. He showed that an equivalent statement of the... 

Re Entry [63], Ref. [63]) In Ref. [63], Dr. Peter Atkins doesn t seem to explicitly state that negative Kelvin temperatures are hotter than ooK, not colder than OK. He admits the possibility of attaining OK via noncyclic processes, but as we showed in Sect. 3. of this chapter purely dynamic — as opposed to thermodynamic — limitations may contravene. On pp. 103-104 of Ref. [63], he correctly states that the third law of thermodynamics is "not really in the same league" as the zeroth, first, and second laws, and that "hints of the Third Law of Thermodynamics are already present in the consequences of the second law," but that the Third Law of Thermodynamics is "the final link in the confirmation that Boltzmann s and Clausius s definitions refer to the same property." But his statement that "we need to do an ever increasing, and ultimately infinite, amount of work to remove energy from a body as heat as its temperature approaches absolute zero" neglects the rapid decrease in specific heat as absolute zero is approached as discussed in Sect. 2. of this chapter. 

In most treatises on thermodynamics, it is usual to refer to the laws of thermodynamics. The conservation of energy is referred to as the First La of Thermodynamics, and this principle was discus.sed in detail in Chapter 3. The positivc-dehniie nature of entropy generation used in Chapter 4, or any of the other statements such as those of Clausius or Kelvin and Planck, are referred to as the Second Law of Thermodynamics. The principle of consers ation of mass precedes the development of thermodynamics. and therefore is not considered to be a law of thermodynamics. 

Any change which occurs in nature is spontaneous and is therefore accompanied by a net increase in entropy. This conclusion led Clausius to his famous concise statement of the laws of thermodynamics ... 

If we imagine the universe to be composed of myriads of such composite systems, in each of which Af/ = 0, then in the aggregate it must also be that AC/ = 0. Thus we have the famous statement of the first law of thermodynamics by Clausius The energy of the universe is a constant. ... 

The main purpose of this book is to present a rigorous and logical discussion of the fundamentals of thermodynamics and to develop in a coherent fashion the application of the basic principles to a number of systems of interest to chemists. The concept of temperature is carefully discussed, and special emphasis is placed on the appropriate method for the introduction of molecular weights into thermodynamics. A new treatment of the second law of thermodynamics is presented which demonstrates that Caratheodory s principle is a necessary and sufficient consequence of the physical statements of Clausius and Kelvin. 

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. 

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. 

We discuss once more the statements of Clausius. The energy of the world is constant. The entropy of the world tends to a maximum. We reformulate now the term world. For a laboratory experiment we think that can simulate a small world, which is a completely isolated thermodynamic system. We do not know what is at the border of the world however, for our laboratory world we think there are no constraints at the border. This idea corresponds to a real world that should be embedded in an empty space. 

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