Law of entropy increase

Perhaps one of the most important consequences of the Boltzmann equation, discovered by Boltzmann himself, was that it led to a kinetic molecular theory basis for the law of entropy increase. This law is contained within the so-called Boltzmann -theorem. Here we will work directly with the Boltzmann entropy Sb rather than the i/-function used in Boltzmann s original work.1 We define a local Boltzmann entropy Ssfri, t) as... 

The systems capability to achieve an equilibrium state has important consequences in terms of so-called irreversible behavior. By irreversible behavior we mean a nonequilibrium system that demonstrates a specific direction or change in a property value, e.g., energy flux for irreversible systems is always in a direction opposite to the temperature gradient. Another example is the law of entropy increase. We will revisit these concepts in Chap. 6 when the transport property flux terms... 

Thus, using the entropy concept, we can give one more rule of the second thermodynamic law the entropy of an isolated thermodynamic system can only increase and, after reaching the maximum value, remain constant. This rule is also referred to as the law of entropy increase. 

Thermodynamics is a deductive science built on the foundation of two fundamental laws that circumscribe the behavior of macroscopic systems the first law of thermodynamics affirms the principle of energy conservation the second law states the principle of entropy increase. In-depth treatments of thermodynamics may be found in References 1—7. 

For a constant polysaccharide mass, an extended (random) coil exposes more surface area than does a helix, and a single helix exposes more than a double helix. The energy content of a polymer molecule is a property of its surface area. Thus, one consequence of a coil-to-helix transition is a diminution of the macromolecular exposed surface area and energy in compliance with the law of entropy. An increase in viscosity coincides with an increase in surface, inasmuch as the resistance to motion covers a wider area. 

As all the natural changes in the universe are irreversible, it may be concluded that the entropy of the universe is ever increasing. The concept of entropy is one of the most important concepts not only in thermodynamics but also in many fields of modern science. The second law of thermodynamics is also called the law of entropy. There is more than one statement of the second law of thermodynamics put forward by scientists as given below (Domkundwar et al. 1985 Nag 2010). 

If the state point moves down from point P or P, the state point is an isentropic curve, which conflicts with the second law of thermodynamics (principle of entropy increase for any spontaneous process). If the state point moves up, it compresses the... 

Not all forms of energy are equivalent with respect to their ability to produce useful work. While heat is conserved, its ability to support a transformation process must decrease according to the second law of thermodynamics (increasing entropy). This is very often neglected when calculating efficiency based only on input and output heat flows (first-law efficiency) and leads to an avoidable waste of still... 

The surfaces in which the paths satisfying the condition = 0 must lie are, thus, surfaces of constant entropy they do not intersect and can be arranged in an order of increasing or decreasmg numerical value of the constant. S. One half of the second law of thennodynamics, namely that for reversible changes, is now established. 

Snch a generalization is consistent with the Second Law of Thennodynamics, since the //theorem and the generalized definition of entropy together lead to the conchision that the entropy of an isolated non-eqnilibrium system increases monotonically, as it approaches equilibrium. 

This completes the heuristic derivation of the Boltzmann transport equation. Now we trim to Boltzmaim s argument that his equation implies the Clausius fonn of the second law of thennodynamics, namely, that the entropy of an isolated system will increase as the result of any irreversible process taking place in the system. This result is referred to as Boltzmann s H-theorem. 

The second law reqmres that the entropy of an isolated system either increase or, in the limit, where the system has reached an equilibrium state, remain constant. For a closed (but not isolated) system it requires that any entropy decrease in either the system or its surroundings be more than compensated by an entropy increase in the other part or that in the Emit, where the process is reversible, the total entropy of the system plus its surroundings be constant. 

Thermodynamic Analyses of Cycles The thermodynamic quahty measure of either a piece of equipment or an entire process is its reversibility. The second law, or more precisely the entropy increase, is an effective guide to this degree of irreversibility. However, to obtain a clearer picture of what these entropy increases mean, it has become convenient to relate such an analysis to the additional work that is required to overcome these irreversibihties. The fundamental equation for such an analysis is... 

According to the second law of thermodynamics, for a reaction to proceed spontaneously it must produce an increase in entropy (AS > 0). Because most spontaneous chemical reactions in the body are exothermic (AH < 0), most spontaneous chemical reactions will have AG values less than zero as well. This means that if, in the reaction shown in Equation... 

Thus, in adiabatic processes the entropy of a system must always increase or remain constant. In words, the second law of thermodynamics states that the entropy of a system that undergoes an adiabatic process can never decrease. Notice that for the system plus the surroundings, that is, the universe, all processes are adiabatic since there are no surroundings, hence in the universe the entropy can never decrease. Thus, the first law deals with the conservation of energy in any type of process, while the sec-... 

This leads to what is called the Clausius form of the second law of thermodynamics. No processes are possible whose only result is the removal of energy from one reservoir and its absorption by another reservoir at a higher temperature. On the other hand, if energy flows from the hot reservoir to the cold reservoir with no other changes in the universe, then the same arguments can be used to show that the entropy increases, nr remains constant for reversible processes. Therefore, such energy flows, which arc vciy familiar, are in agreement with the laws of thermodynamics. 

The second law of thermodynamics states that energy exists at various levels and is available for use only if it can move from a higher to a lower level. For example, it is impossible for any device to operate in a cycle and produce work while exchanging heat only with bodies at a single fixed temperature. In thermodynamics, a measure of the unavailability of energy has been devised and is known as entropy. As a measure of unavailability, entropy increases as a system loses heat, but remains constant when there is no gain or loss of heat as in an adiabatic process. It is defined by the following differential equation ... 

At first sight, self-organization appears to violate the Second Law of Thermodynamics, which asserts that the entropy S of an isolated system never decreases (or, more formally, > 0) see figure 11.2-a. Since entropy is essentially a measure of the degree of disorder in a system, the Second Law is usually interpreted to mean that an isolated system will become increasingly more disordered with time. How, then, can structure emerge after a system has had a chance to evolve ... 

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. 

The second law of thermodynamics essentially states that the entropy of a thermodynamic system always increases with time,... 

The relationship between entropy change and spontaneity can be expressed through a basic principle of nature known as the second law of thermodynamics. One way to state this law is to say that in a spontaneous process, there is a net increase in entropy, taking into account both system and surroundings. That is,... 

Second law of thermodynamics A basic law of nature, one form of which states that all spontaneous processes occur with an increase in entropy, 457 Second order reaction A reaction whose rate depends on the second power of reactant concentration, 289,317q gas-phase, 300t... 

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