Clausius principle

THEORETICAL LIMITS ON PERPETUAL MOTION KELVIN S AND CLAUSIUS PRINCIPLES... 

The statement of the Carnot-Clausius Principle is then the following ... 

Statement of Carnot and Clausius principle for an open reversible transformation. Entropy, 80.—68. Entropy of a perfect gas,... 

The second law as it left the hands of Carnot required no explanation. On the caloric theory then prevalent, it was a necessary consequence of a hydrodynamical analogy—the mechanical explanation was in fact, as Carnot s words show, the source of the principle. When the caloric theory was thrown down, the analogy and explanation fell with it, and the reconstruction of Carnot s principle by Clausius and Kelvin resulted in a law of experience. 

The second general principle is based on the properties of the entropy function, and is contained in the aphorism of Clausius... 

The Clausius and Kelvin-Planck statements and the Carnot principle reflect a historical interest in increasing the efficiency of engines. While the... 

Of course, depending on the system, the optimum state identified by the second entropy may be the state with zero net transitions, which is just the equilibrium state. So in this sense the nonequilibrium Second Law encompasses Clausius Second Law. The real novelty of the nonequilibrium Second Law is not so much that it deals with the steady state but rather that it invokes the speed of time quantitatively. In this sense it is not restricted to steady-state problems, but can in principle be formulated to include transient and harmonic effects, where the thermodynamic or mechanical driving forces change with time. The concept of transitions in the present law is readily generalized to, for example, transitions between velocity macrostates, which would be called an acceleration, and spontaneous changes in such accelerations would be accompanied by an increase in the corresponding entropy. Even more generally it can be applied to a path of macrostates in time. 

One hundred fifty years ago, the two classic laws of thermodynamics were formulated independently by Kelvin and by Clausius, essentially by making the Carnot theorem and the Joule-Mayer-Helmholtz principle of conservation of energy concordant with each other. At first the physicists of the middle 1800s focused primarily on heat engines, in part because of the pressing need for efficient sources of power. At that time, chemists, who are rarely at ease with the calculus, shied away from... 

The vap. press, curve of solid iodine is indicated by PO, Fig. 16 that of liquid iodine by 00 and the effect of press, on the m.p. of iodine by ON. At the triple point 0 these curves meet. Fig. 18 shows a similar curve for water. The curve PO thus represents the sublimation curve or hoar-frost line OC. the boiling or vaporization curve, i.e. the effect of press, on the b.p. of the liquid. The same phenomenon occurs with water, iodine, etc., and the principle involved is the same as indicated in the law represented by Clapeyron-Clausius equations with respect to the lowering of the m.p. by an increase of press. Consequently, if the vap. press, of iodine be less than that of th,e triple point, the solid does not melt, but rather sublimes directly without melting at the triple point at 114-15° (89 8 mm.) and A. von Richter at 116 1° (90 mm.). According to R. W. Wood, if the condensation of iodine vapour occurs above —60°, a black granular deposit is formed, but below that temp, a deep red film is produced. 

Clausius great paper of 1850 can be recognized as a landmark in the development of thermodynamics. As remarked by Thomson in 1851, the merit of first establishing [Carnot s theorem] upon correct principles is entirely due to Clausius. In his 1889 eulogy of Clausius, Gibbs praised the 1850 paper in the following terms ... 

The simple inequality (4.10) captures the essence of the second law. Its general consistency with universal inductive experience will be established in Section 4.4, and its further consequences (culminating in the final form of the second law as expressed by Clausius) will be developed in Sections 4.5-4.7. Thus, Carnot s remarkable principle provides virtually complete answers to the questions posed at the beginning of this chapter, although the relationship of (4.10) to these broader issues will certainly not become obvious until the following section. 

Carnot s principle (4.10) may not seem particularly compelling from experience. However, we can easily derive some consequences from (4.10) that are indeed more obvious statements about the irreversibility of natural events, and hence provide compelling inductive proof of the truth of Carnot s principle. These derivative principles were first obtained by Thomson (Kelvin) and Clausius. 

Principle of Clausius It is impossible to devise an engine that, working in a cycle, shall produce no effect other than the transfer of heat from a colder to a hotter body. 

Again we conclude that Carnot s principle must be true, because devices that contradict the principle of Clausius are never observed. 

From a purely phenomenological point of view, this expression of the conservation of energy may be considered the definition ul the heat received by the system. The extension of the mechanical principle of conservation of energy to include the flow of heat is due mainly to Carnot. Joule. Helmholtz, and Clausius. 

In the 19th century the variational principles of mechanics that allow one to determine the extreme equilibrium (passing through the continuous sequence of equilibrium states) trajectories, as was noted in the introduction, were extended to the description of nonconservative systems (Polak, 1960), i.e., the systems in which irreversibility of the processes occurs. However, the analysis of interrelations between the notions of "equilibrium" and "reversibility," "equilibrium processes" and "reversible processes" started only during the period when the classical equilibrium thermodynamics was created by Clausius, Helmholtz, Maxwell, Boltzmann, and Gibbs. Boltzmann (1878) and Gibbs (1876, 1878, 1902) started to use the terms of equilibria to describe the processes that satisfy the entropy increase principle and follow the "time arrow."... 

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. 

The two methods described for determining vapor pressures appear to give reliable vapor pressure data for volatile pesticides and fumigants. The precision is better than 10 to 20% in most cases. Care must be taken, particularly with the determination of low vapor pressures which can be difficult. Estimation of vapor pressures by Clausius-Clapeyron and other related functions is dependable for interpolation and limited extrapolation. Extensive extrapolation is, as always, dangerous, and a direct measurement should be made as closely as possible to the desired temperature. The literature contains a number of examples which violate this principle. 

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