Entropy and second law of thermodynamics

In irreversible thermod3mamics, the second law of thermodynamics dictates that entropy of an isolated system can only increase. From the second law of thermodynamics, entropy production in a system must be positive. When this is applied to diffusion, it means that binary diffusivities as well as eigenvalues of diffusion matrix are real and positive if the phase is stable. This section shows the derivation (De Groot and Mazur, 1962). 

It seems enigmatic that we often struggle so hard to achieve desired separations when the basic concept of moving one component away from another is inherently so simple. Much of the difficulty arises because separation flies in the face of the second law of thermodynamics. Entropy is gained in mixing, not in separation. Therefore it is the process of mixing that occurs spontaneously. To combat this and achieve separation, one must apply and manipulate external work and heat and allow dilution in a... 

Statement of the Second Law of Thermodynamics Entropy Changes and Entropy Creation. 

C is correct. Chemist A chooses the direction of the reaction based upon chemical stability, and then says that the direction will change at higher temperatures. This is tantamount to saying that the stability will switch at higher temperatures, which, by the way, is also correct. D is, of course, a false statement. The entropy shown for Reaction 1 is the entropy of the reaction. In other words, it is the entropy of the system, and not the entropy of the universe. Chemist A s statement is correct, and does not contradict the second law of thermodynamics. A and B are contradicted because Chemist A says the direction is temperature dependent. 

Other useful sources of historical information are The Early Development of the Concepts of Temperature and Heat The Rise and Decline of the Caloric Theory by D. Roller in Volume 1 of Harvard Case Histories in Experimental Science edited by J.B. Conant and published by Harvard University Press in 1957 articles in Physics Today, such as A Sketch for a History of Early Thermodynamics by E. Mendoza (February, 1961, p.32), Carnot s Contribution to Thermodynamics by M.J. Klein (August, 1974, p. 23) articles in Scientific American and various books on the history of science. Of special interest is the book The Second Law by P.W. Atkins published by Scientific American Books, W.H. Freeman and Company (New York, 1984) which contains a very extensive discussion of the entropy, the second law of thermodynamics, chaos and symmetry. 

According to the second law of thermodynamics, entropy production must be positive. Consequently, the graph of the constitutive relation must be within the first and third quadrant. 

Although the forgoing research works have covered a wide range of problems involving the flow and heat transfer of viscoelastic fluid over stretching surface they have been restricted, from thermodynamic point of view, to only the first law analysis. The contemporary trend in the field of heat transfer and thermal design is the second law of thermodynamics analysis and its related concept of entropy generation minimization. 

The Carnot cycle is formulated directly from the second law of thermodynamics. It is a perfectly reversible, adiabatic cycle consisting of two constant entropy processes and two constant temperature processes. It defines the ultimate efficiency for any process operating between two temperatures. The coefficient of performance (COP) of the reverse Carnot cycle (refrigerator) is expressed as... 

Macroscopic and Microscopic Balances Three postulates, regarded as laws of physics, are fundamental in fluid mechanics. These are conservation of mass, conservation of momentum, and con-servation of energy. In addition, two other postulates, conservation of moment of momentum (angular momentum) and the entropy inequality (second law of thermodynamics) have occasional use. The conservation principles may be applied either to material systems or to control volumes in space. Most often, control volumes are used. The control volumes may be either of finite or differential size, resulting in either algebraic or differential consei vation equations, respectively. These are often called macroscopic and microscopic balance equations. 

The second law of thermodynamics may be used to show that a cyclic heat power plant (or cyclic heat engine) achieves maximum efficiency by operating on a reversible cycle called the Carnot cycle for a given (maximum) temperature of supply (T ax) and given (minimum) temperature of heat rejection (T jn). Such a Carnot power plant receives all its heat (Qq) at the maximum temperature (i.e. Tq = and rejects all its heat (Q ) at the minimum temperature (i.e. 7 = 7, in) the other processes are reversible and adiabatic and therefore isentropic (see the temperature-entropy diagram of Fig. 1.8). Its thermal efficiency is... 

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 ... 

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). 

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,... 

The third approach is called the thermodynamic theory of passive systems. It is based on the following postulates (1) The introduction of the notion of entropy is avoided for nonequilibrium states and the principle of local state is not assumed, (2) The inequality is replaced by an inequality expressing the fundamental property of passivity. This inequality follows from the second law of thermodynamics and the condition of thermodynamic stability. Further the inequality is known to have sense only for states of equilibrium, (3) The temperature is assumed to exist for non-equilibrium states, (4) As a consequence of the fundamental inequality the class of processes under consideration is limited to processes in which deviations from the equilibrium conditions are small. This enables full linearization of the constitutive equations. An important feature of this approach is the clear physical interpretation of all the quantities introduced. 

This result holds equally well, of course, when R happens to be the operator representing the entropy of an ensemble. Both Tr Wx In Wx and Tr WN In WN are invariant under unitary transformations, and so have no time dependence arising from the Schrodinger equation. This implies a paradox with the second law of thermodynamics in that apparently no increase in entropy can occur in an equilibrium isolated system. This paradox has been resolved by observing that no real laboratory system can in fact be conceived in which the hamiltonian is truly independent of time the uncertainty principle allows virtual fluctuations of the hamiltonian with time at all boundaries that are used to define the configuration and isolate the system, and it is easy to prove that such fluctuations necessarily increase the entropy.30... 

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