Thermodynamic definition of entropy

The material covered in this chapter is self-contained, and is derived from well-known relationships such as Newton s second law and the ideal gas law. Some quantum mechanical results and the statistical thermodynamics definition of entropy are given without rigorous derivation. The end result will be a number of practical formulas that can be used to calculate thermodynamic properties of interest. 

The next important thermodynamic function that we must obtain is the entropy S. The statistical thermodynamic definition of entropy is... 

The thermodynamic definition of entropy says that the change in entropy dS in a process carried out reversibly is the heat absorbed in the process d Qrev divided by the temperature... 

The successful development of the thermodynamics of irreversible phenomena depends on the possibility of an explicit evaluation of the production of entropy, and for this it is necessary to assume that the thermodynamic definition of entropy can be applied equally to systems which are not in equilibrium, that is to states whose mean lifetime is limited. We are thus confronted immediately with the problem of the domain of validity of the thermodynamic treatment of irreversible phenomena, which can be determined only by a comparison of the results of the thermodynamic treatment with those obtained by the use of statistical mechanics. This problem wall be dealt with in more detail in the third volume of this work meanwhile the main conclusions can be summarized as follows. 

The Entropy Change for a Process Can Be Calculated Using the Thermodynamic Definition of Entropy 432... 

In general, the thermodynamic definition of entropy (Equations 8.6 to 8.8) yields the same value for the entropy change of a process as Boltzmann s statistical definition (Equation 8.3) for the same process. Consider, for example, the entropy change in the reversible and isothermal (constant teinperature) mmqn n i n i les of an ideal gas from an initial volume Vi to a inB39B9tft0-6K ile heat... 

We learned at the end of Section 8.1 [recall Figure 8.5(d)] that the entropy of a system increases when the temperature of the system is raised from Ti to T2. Using the thermodynamic definition of entropy, we can calculate the change in entropy for a system upon heating (or cooling). Beginning with Equation 8.6,... 

The thermodynamic definition of entropy can be used to calculate changes in entropy on expansion or contraction, heating or cooling, or as a result of a phase change. 

Use the thermodynamic definition of entropy and the second law to explain why heat cannot flow spontaneously from a region of low temperature to one of higher temperature. 

Equation (7.45) is sometimes called the thermodynamic definition of entropy. It shows how to obtain the entropy change (w hich you cannot otherwise measure directly) from experimentally observable quantities (heat transfer and temperature) by using a quasi-static process. 

The second and third laws of thermodynamics The second law and the definition of entropy... 

GENERAL EQUATIONS FOR THE ENTROPY OF GASES 143 conclude from Equation (6.111) that a natural thermodynamic definition of T is... 

Traditional thermodynamics gives a clear definition of entropy but unfortunately does not tell us what it is. An idea of the physical nature of entropy can be gained from statistical thermodynamics. Kelvin and Boltzmann recognised diat there was a relationship between entropy and probability (cf., disorder) of a system with the entropy given by... 

The term entropy, which literally means a change within, was first used in 1851 by Rudolf Clausius, one of the formulators of the second law of thermodynamics. A rigorous quantitative definition of entropy involves statistical and probability considerations. However, its nature can be illustrated qualitatively by three simple examples, each demonstrating one aspect of entropy. The key descriptors of entropy are randomness and disorder, manifested in different ways. 

Chapter 5 gives a microscopic-world explanation of the second law, and uses Boltzmann s definition of entropy to derive some elementary statistical mechanics relationships. These are used to develop the kinetic theory of gases and derive formulas for thermodynamic functions based on microscopic partition functions. These formulas are apphed to ideal gases, simple polymer mechanics, and the classical approximation to rotations and vibrations of molecules. 

The classical definition of entropy based on the second law of thermodynamics has given the total differential of entropy in the form of dQrev / / . With a reversible heat transfer into a closed system receiving a differential amount of heat dQrev, the system changes its entropy by the differential amount of dS as shown in Eq. 3.8 ... 

Thermodynamics — deals with the interrelations between -> energy and matter and the laws that govern them. The energetic changes in a system are governed by the fundamental laws of thermodynamics, which have been deduced directly from experience. The first law of thermodynamics simply states the principle of conservation of energy. The second law of thermodynamics states whether or not a process takes place in one or the other direction. For instance, heat always spontaneously flows from a higher temperature body to another one with lower temperature and never in the opposite direction. The second law of thermodynamics provides the definition of -> entropy. The third law of thermodynamics, also known as -> Nernsfs theorem, states the possibility... 

Similarly, if one is interested in a macroscopic thermodynamic state (i.e., a subset of microstates that corresponds to a macroscopically observable system with bxed mass, volume, and energy), then the corresponding entropy for the thermodynamic state is computed from the number of microstates compatible with the particular macrostate. All of the basic formulae of macroscopic thermodynamics can be obtained from Boltzmann s definition of entropy and a few basic postulates regarding the statistical behavior of ensembles of large numbers of particles. Most notably for our purposes, it is postulated that the probability of a thermodynamic state of a closed isolated system is proportional to 2, the number of associated microstates. As a consequence, closed isolated systems move naturally from thermodynamic states of lower 2 to higher 2. In fact for systems composed of many particles, the likelihood of 2 ever decreasing with time is vanishingly small and the second law of thermodynamics is immediately apparent. 

This is a crude model, but hopefully you now see how the calculus of probabilities, as Maxwell put it, explains why heat flows downhill (from hot to cold), why a gas expands to occupy its container and why the world is. . . getting more disordered and generally going to hell in a hand-basket We also hope that you now have a feel for entropy that cannot be obtained from the purely thermodynamic definition of heat divided by temperature, hi principle, calculating the entropy of a system would now seem to be easy. Just count the num-... 

This very important relationship is the macroscopic (thermodynamic) definition of AS. In our treatment we started with the definition of entropy based on probability, because that definition better emphasizes the fundamental character of entropy. However, it is also very important to know how entropy changes relate to changes in macroscopic properties, such as volume and heat, because these changes are relatively easy to measure. 

A thermodynamic definition of microemulsions can be obtained from a consideration of the energy and entropy terms for formation of microemulsions. The process of formation of microemuision from a bulk oil phase (for a O/W microemuision) or from a bulk water phase (for a W/O microemuision) is shown schematically in Figure 15.2. 

From the scientific definition point of view, there is a slight difference between our continuum thermodynamics definition of the Second Law and its statistical mechanical version so that the continuum thermodynamics definition of the Second Law states that an observation of decreased universal entropy is impossible in isolated systems however the statistical mechanical definition says that an observation of universal increased entropy is not probable. 

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