Entropy second law and

Before we go on to calculate entropy changes for specific processes there are three matters which have been raised that we 

This condition indicates that spontaneous processes are accompanied by an overall increase in the total entropy, A un erse- 

Also from Frame 13 we have an equation for calculating entropy change in the form  

Alternatively, consider now an endothermic reaction for which A//system 0 (i.e. positive), the heat now lost from the surroundings, r/surroundings which will be treated as being negative (since we are treating the surroundings as our system, for the moment) and will be equal to —AHsystem (which is a negative quantity), thus we have  

Since for a thermodynamic system, qmY is the heat added reversibly, then  

Reversible processes do not occur in nature and, in any case, as we have seen (Frame 9) they would take an infinite amount of time for completion. They rather represent the limit of irreversible changes much as in the case of the gas expansion discussion (Frame 9) when maximum work was involved at this limit of reversibility. 

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Equation (A2.1.21) includes, as a special case, the statement dS > 0 for adiabatic processes (for which Dq = 0) and, a fortiori, the same statement about processes that may occur in an isolated system (Dq = T)w = 0). If the universe is an isolated system (an assumption that, however plausible, is not yet subject to experimental verification), the first and second laws lead to the famous statement of Clausius The energy of the universe is constant the entropy of the universe tends always toward a maximum. ... 

By the standard methods of statistical thermodynamics it is possible to derive for certain entropy changes general formulas that cannot be derived from the zeroth, first, and second laws of classical thermodynamics. In particular one can obtain formulae for entropy changes in highly di.sperse systems, for those in very cold systems, and for those associated, with the mixing ofvery similar substances. 

The fundamental thermodynamic properties that arise in connection with the first and second laws of thermodyuamics are internal energy and entropy These properties, together with the two laws for which they are essential, apply to all types of systems. However, different types of systems are characterized by different sets of measurable coordinates or variables. The type of system most commonly... 

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. 

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). 

In Chapter 1 we described the fundamental thermodynamic properties internal energy U and entropy S. They are the subjects of the First and Second Laws of Thermodynamics. These laws not only provide the mathematical relationships we need to calculate changes in U, S, H,A, and G, but also allow us to predict spontaneity and the point of equilibrium in a chemical process. The mathematical relationships provided by the laws are numerous, and we want to move ahead now to develop these equations.1... 

As with the first and second laws, the Third Law is based on experimental measurements, not deduction. It is easy, however, to rationalize such a law. In a perfectly ordered3 crystal, every atom is in its proper place in the crystal lattice. At T— 0 Kelvin, all molecules are in their lowest energy state. Such a configuration would have perfect order and since entropy is a measure of the disorder in a system, perfect order would result in an entropy of zero.b Thus, the Third Law gives us an absolute reference point and enables us to assign values to S and not just to AS as we have been restricted to do with U, H, A, and G. 

A simple statement of the Second Law is natural processes are accompanied by an increase in the entropy of the universe. There are several other statements of the Second Law in the chapter Notes. As noted above, entropy is a measure of disorder the greater the extent of disorder, the greater the entropy. The Second Law tells us that things change spontaneously in a way that increases disorder. At equilibrium, entropy is maximized and disorder reigns. 

It is more problematical to define the third law of thermodynamics compared to the first and second laws. Experimental work by Richards (1902) and Nemst (1906) led Nemst to postulate that, as the temperature approached absolute zero, the entropy of the system would also approach zero. This led to a definition for the third law of thermodynamics that at a temperature of absolute zero the entropy of a condensed system would also be zero. This was further refined by Planck (1911) who suggested this be reworded as the entropy of a pure element or substance in a perfect crystalline form is zero at absolute zero. 

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 only two functions actually required in thermodynamics are the energy function, obtained from the first law of thermodynamics, and the entropy function, obtained from the second law of thermodynamics. However, these functions are not necessarily the most convenient functions. The enthalpy function was defined in order to make the pressure the independent variable, rather than the volume. When the first and second laws are combined, as is done in this chapter, the entropy function appears as an independent variable. It then becomes convenient to define two other functions, the Gibbs and Helmholtz energy functions, for which the temperature is the independent variable, rather than the entropy. These two functions are defined and discussed in the first part of this chapter. 

By applying the first and second laws to processes in which heat and work are exchanged with the environment at P0, T0, we have shown before that this generated entropy is associated with a loss of work according to... 

Fundamental equation 2.2-8 has been presented as the equation resulting from the first and second laws, but thermodynamic treatments can also be based on the entropy as a thermodynamic potential. Equation 2.2-8 can alternatively be written as... 

The Second Law is sometimes stated as the Entropy Law. Entropy is a measure of randomness or disorder in a system. Systems that are more randomized, chaotic, or evenly mixed have more entropy. The Second Law states the entropy of the universe is constantly increasing. One clear implication of the Second Law is that the universe never, and a system almost never, spontaneously becomes more organized. So, hot molecules will not spontaneously separate themselves from cold molecules. Mixtures of oxygen and nitrous oxide will not spontaneously separate and send the oxygen to the patient separately from the nitrous oxide. IV fluids will mix evenly throughout the circulatory system, and not congregate in just the left arm. 

The combined first and second laws of thermodynamics state how an increment of mechanical work (fdX = dW) done on the system can produce an increase in the internal energy dE or a decrease in the entropy ... 

However, using entropy as a criterion of whether a biochemical process can occur spontaneously is difficult, as the entropy changes of chemical reactions are not readily measured, and the entropy change of both the system and its surroundings must be known. These difficulties are overcome by using a different thermodynamic function, free energy (G), proposed by Josiah Willard Gibbs which combines the first and second laws of thermodynamics ... 

Before continuing, let us decide to define a new thermodynamic function that measures energy degradation. We will call this function the entropy and designate it by the symbol S. In terms of entropy our second law becomes... 

We cannot write down a priori a generic balance relation for the entropy of a fluid. We can, however, derive a result that can be placed in the same form as Eq. (3) and therefore recognized as a balance relation. By working with the combined first and second laws of thermodynamics, one... 

There were many different ways in which the second law was expressed, and it is not always obvious that they are mathematically equivalent. William Thomson, Lord Kelvin (1824-1907), stated the law this way in 1851 It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. In 1865 Rudolf Clausius (1822-88) expressed the first and second laws of thermodynamics as follows The energy of the universe is constant the entropy tends towards a maximum. Entropy was a term invented by Clausius, and it became absolutely central to the understanding and expression of thermodynamics. 

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