THE SECOND LAW OF THERMODYNAMICS

Second Law of Thermodynamics. The entropy change of any system together with its surroundings is positive for a real process, approaching zero as the process approaches reversibiUty ... 

The foUowiag criterion of phase equUibrium can be developed from the first and second laws of thermodynamics the equUibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

As pointed out in Section 2.4, shock waves are such rapid processes that there is no time for heat to flow into the system from the surroundings they are considered to be adiabatic. By the second law of thermodynamics, the quantity (S — Sg) must be positive for any thermodynamic process in an isolated system. According to (2.54), this quantity can only be positive if the P-V isentrope is concave upward. Thus, the thermodynamic stability condition for a shock wave is... 

The earliest hint that physics and information might be more than just casually related actually dates back at least as far as 1871 and the publication of James Clerk Maxwell s Theory of Heat, in which Maxwell introduced what has become known as the paradox of Maxwell s Demon. Maxwell postulated the existence of a hypothetical demon that positions himself by a hole separating two vessels, say A and B. While the vessels start out being at the same temperature, the demon selectively opens the hole only to either pass faster molecules from A to B or to pass slower molecules from B to A. Since this results in a systematic increase in B s temperature and a lowering of A s, it appears as though Maxwell s demon s actions violate the second law of thermodynamics the total entropy of any physical system can only increase, or, for totally reversible processes, remain the same it can never decrease. Maxwell was thus the first to recognize a connection between the thermodynamical properties of a gas (temperature, entropy, etc.) and the statistical properties of its constituent molecules. 

Our most important insight into the connection between thermodynamics and black holes comes from a celebrated result obtained by Bardeen, Carter and Hawking [bard73], that the four laws of black hole physics can be obtained by replacing, in the first and second laws of thermodynamics, the entropy and temperature of a thermodynamical system by the black hole event horizon (or boundary of the black hole) and surface gravity (which measures the strength of the gravitational field at the black hole s surface). 

It follows from the second law of thermodynamics, the Onsager relation Ltj = Lji, the thermodynamic stability condition (G3)... 

The pattern we have identified is one version of the second law of thermodynamics. The natural progression of a system and its surroundings (which together make up the universe") is from order to disorder, from lower to higher entropy. For practical measurements, a small isolated region, such as a thermally insulated, sealed flask or a calorimeter, is considered to represent the universe. 

Entropy is a measure of disorder according to the second law of thermodynamics, the entropy of an isolated system increases in any spontaneous process. Entropy is a state function. 

We have already stated that some defects are related to the entropy of the solid, and that a perfeet solid would violate the second law of thermodynamics. The 2nd law states that zero entropy is only possible at absolute zero temperature. However, most solids exist at temperatures far above absolute zero. Thus, most of the solids that we eneounter are defeet-solids. The defects are usually "point defeets", which are atomlstie... 

These bounds originate from the systematic errors (biases) due to the finite sampling in free energy simulations and they differ from other inequalities such as those based on mathematical statements or the second law of thermodynamics. The bounds become tighter with more sampling. It can be shown that, statistically, in a forward calculation AA(M) < AA(N) for sample sizes M and N and M > N. In a reverse calculation, AA(M) > AA(N). In addition, one can show that the inequality (6.27) presents a tighter bound than that of the second law of thermodynamics... 

Consider a thermodynamic system with an external parameter (or constraint) A that can be used to control the state of the system. When changing the control parameter A a certain amount of work is performed on the system. According to the second law of thermodynamics the average work necessary to do that is smaller than the Helmholtz free energy difference between the two equilibrium states corresponding to the initial and final values of the constraint [33]... 

Second Law of Thermodynamics The Second Law of Thermodynamics states that all processes that occur spontaneously move in the direction of an increase in entropy of the universe (system + surroundings). 

Ions or molecules flowing down their concentration gradients is one aspect of a very general statement known as the Second Law of Thermodynamics. The Second Law is a mathematical statement to the effect that all real processes increase the disorder, captured in a quantity known as entropy, of the universe. Entropy is a measure of disorder or randomness and may be thought of as negative information. 

The Carnot cycle is of historical importance. The reversible cycle was introduced by a French engineer N.S. Carnot in 1824 and led to the development of the second law of thermodynamics. The importance of the Carnot cycle is that it sets up a standard thermal cycle performance for the actual cycles to compare with. 

Developments in FTs. FTs are simple results that provide a new view to better understanding issues related to irreversibility and the second law of thermodynamics. The main assumption of FTs is microscopic reversibility or local equilibrium, an assumption that has received some criticism [192-194]. Establishing limitations on the validity of FTs is the next task for the future. At present, no experimental result contradicts any of the FTs, mainly because the underlying assumptions are respected in the experiments or because current techniques are not accurate enough to detect systematic discrepancies. Under some experimental conditions, we... 

The equilibrium conditions for phase equilibria can be derived in the simplest way using the Gibbs energy G. According to the second law of thermodynamics, the total Gibbs energy of a closed system at constant temperature and pressure is minimum at equilibrium. If this condition is combined with the condition that the total number of moles of component i is constant in a closed system... 

Gas chromatography involves chemical equilibria between phases to bring about a particular separation. Thus, a brief discussion of phase equilibria is pertinent at this point. Phase equilibria separations can be understood with the use of the second law of thermodynamics. The phase rule states that if we have a system of C components which are distributed between. P phases, the composition of each of these phases will be completely defined by C-l concentration terms. Thus, to have the compositions of P phases defined it is necessary to have P(C-l) concentration terms. The temperature and pressure also are variables and are the same for all the phases. Assuming no other forces influence the equilibria it follows that. 

Thermodynamics comprises a field of knowledge that is fundamental and applicable to a vast area of human experience. It is a study of the interactions between two or more bodies, the interactions being described in terms of the basic concepts of heat and work. These concepts are deduced from experience, and it is this experience that leads to statements of the first and second laws of thermodynamics. The first law leads to the definition of the energy function, and the second law leads to the definition of the entropy function. With the experimental establishment of these laws, thermodynamics gives an elegant and exact method of studying and determining the properties of natural systems. 

The equilibrium aspect of micelle formation can be considered by application of the second law of thermodynamics. The equilibrium constant for the process represented by Eq. (3) is given by... 

Second law of thermodynamics The entropy of the universe increases in a spontaneous process i.e., the entropy of the universe is always increasing. 

Equation (13.15) is analogous to our earlier equation (2.27), Frame 2, relating to the Second Law of Thermodynamics. The argument above should not, however, be regarded as a proof of the Second Law equation but rather regarded as a convienient further introduction of the same idea. 

In an irreversible process, in conformity with the second law of thermodynamics, the magnitude that determines the time dependence of an isolated thermodynamic system is the entropy, S [23-26], Consequently, in a closed system, processes that merely lead to an increase in entropy are feasible. The necessary and sufficient condition for a stable state, in an isolated system, is that the entropy has attained its maximum value [26], Therefore, the most probable state is that in which the entropy is maximum. 

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