Clausius spontaneous change

In the equilibrium Second Law, the first entropy increases during spontaneous changes in structure, and when the structure stabilizes (i.e., change ceases), the first entropy is a maximum. This state is called the equilibrium state. Similarly, in the nonequilibrium Second Law, the second entropy increases during spontaneous changes in flux, and when the flux stabilizes, the second entropy is a maximum. This state is called the steady state. The present nonequilibrium Second Law has the potential to provide the same basis for the steady state that Clausius Second Law has provided for the equilibrium state. 

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. 

The second law of thermodynamics (Clausius formulation) In isolated systems, spontaneous changes are always accompanied by a net increase in entropy. 

Let us first introduce a useful short-cut to the constrained optimization procedure employed in Section 5.2, based on the general Clausius inequality [cf. (4.43)] for spontaneous changes toward equilibrium ... 

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]

Clausius introduced the entropy if a quantity of heat Q is reversibly absorbed by a system at the absolute temperature T, the increase of entropy is AS=Q/T. In spontaneous changes the entropy of a system increases and reaches a maximum, whilst the free energy decreases to a minimum, in stable equilibrium. The entropy was first used in chemical problems by Horstmann. J. W. Gibbs (following earlier publications by Massieu and MaxwelF) and Duhem, made use of three thermodynamic functions ... 

If we treat the universe as an isolated system (although cosmology provides no assurance that this is a valid concept), we can say that as spontaneous changes occur in the universe, its entropy continuously increases. Clausius summarized the first and second laws in a famous statement Die Energie der Welt ist constant die Entropie der Welt strebt einem Maximum zu (the energy of the universe is constant the entropy of the universe strives toward a maximum). 

Clausius s Ideas Absolute Entropies 13-4 Criterion for Spontaneous Change The Second Law of Thermodynamics... 

A third statement of the second law is based on the entropy. In reversible systems all forces must be opposed by equal and opposite forces. Consequently, in an isolated system any change of state by reversible processes must take place under equilibrium conditions. Changes of state that occur in an isolated system by irreversible processes must of necessity be spontaneous or natural processes. For all such processes in an isolated system, the entropy increases. Clausius expressed the second law as The entropy of the universe is always increasing to a maximum. Planck has given a more general statement of the second law Every physical and chemical process in nature takes place in such a way as to increase the sum of the entropies of all bodies taking any part in the process. In the limit, i.e., for reversible processes, the sum of the entropies remains unchanged. 

The First Law of fhermodynamics (colloquially, the law of conservation of energy Mayer, Helmholtz) does not explain why or guarantee that a defined system change will occur spontaneously or, if it does, in which direction the change will occur. This shortcoming is addressed by the Second Law of fhermodynamics. Again, a vast amount of experience and experimentation can be generahzed by (Carnot, Kelvin, Clausius),... 

This is known as the Clausius inequality and has important applications in irreversible processes. For example, dS > (dQ/T) for an irreversible chemical reaction or material exchange in a closed heterogeneous system, because of the extra disorder created in the system. In summary, when we consider a closed system and its surroundings together, if the process is reversible and if any entropy decrease takes place in either the system or in its surroundings, this decrease in entropy should be compensated by an entropy increase in the other part, and the total entropy change is thus zero. However, if the process is irreversible and thus spontaneous, we should apply Clausius inequality and can state that there is a net increase in total entropy. Total entropy change approaches zero when the process approaches reversibility. 

Clausius, in 1850, invented the term entropy for the ratio of the heat content of an isolated system to its absolute temperature. He showed that in any spontaneous energy change the entropy of the system would increase. This principle is called the second law of thermodynamics. 

The second law specifies that heat will not pass spontaneously from a colder to a hotter body without some change in the system. Or, as Planck himself generalized it in his Ph.D. dissertation at the University of Munich in 1879, that the process of heat conduction cannot be completely reversed by any means. Besides forbidding the construction of perpetual-motion machines, the second law defines what Planck s predecessor Rudolf Clausius named entropy because energy dissipates as heat whenever work is done—heat that cannot be collected back into useful organized form—the universe must slowly run down to randomness. This vision of increasing disorder means that the universe is one-way and not reversible the second law is the expression in physical form of what we call time. But the equations of mechanical physics—of what is now called classical physics—... 

The second law of thermodynamics as stated by Clausius in 1854 concerns the spontaneous evolution of a system subject to processes. It defines the entropy of a system, which is related to the change in heat during the process and the temperature by the relation... 

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