Chemistry
Absolute Entropy and Entropy Change
Absolute entropy is a measure of the amount of disorder or randomness in a system at 0 Kelvin. Entropy change refers to the change in the level of disorder or randomness in a system as a result of a chemical reaction or physical process. It is a key concept in thermodynamics and is related to the dispersal of energy in a system.
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11 Key excerpts on "Absolute Entropy and Entropy Change"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
The second law of thermodynamics states that entropy in the combination of a system and its surroundings (or in an isolated system by itself) increases during all spontaneous chemical and physical processes. The Clausius equation of δ q rev / T = Δ S introduces the measurement of entropy change, Δ S . Entropy change describes the direction and quantifies the magnitude of simple changes such as heat transfer between systems – always from hotter to cooler spontaneously. Thus, when a mole of substance at 0 K is warmed by its surroundings to 298 K, the sum of the incremental values of q rev / T constitute each element's or compound's standard molar entropy, a fundamental physical property and an indicator of the amount of energy stored by a substance at 298 K. Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture. Entropy is equally essential in predicting the extent of complex chemical reactions, i.e. whether a process will go as written or proceed in the opposite direction. For such applications, Δ S must be incorporated in an expression that includes both the system and its surroundings, Δ S universe = Δ S surroundings + Δ S system . This expression becomes, via some steps, the Gibbs free energy equation for reactants and products in the system: Δ G [the Gibbs free energy change of the system] = Δ H [the enthalpy change] − T Δ S [the entropy change]. Entropy balance equation for open systems In chemical engineering, the principles of thermodynamics are commonly applied to open systems, i.e. those in which heat, work, and mass flow across the system boundary. In a system in which there are flows of both heat ( ) and work, i.e. (shaft work) and P(dV/dt) (pressure-volume work), across the system boundaries, the heat flow, but not the work flow, causes a change in the entropy of the system.
eBook - PDF- Young, William Vining, Roberta Day, Beatrice Botch(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
In all cases, Interactive Figure 20.1.1 Explore directionality in chemical processes. 1 2 3 Hydrogen balloon explosion sequence Charles D. Winters Figure 20.1.2 A nonspontaneous process: splitting water into hydrogen and oxygen Charles D. Winters Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 Unit 20 Thermodynamics: Entropy and Free Energy 634 these terms refer to the random molecular energy within a system in the form of trans-lational, rotational, and vibrational motion of the particles. Increasing the temperature increases the random motion of the particles within a substance and, thus, increases its entropy. Spontaneous change always occurs in the direction of increasing total entropy. An iso-lated system, one that cannot exchange matter or energy with the surroundings (imagine a thermos bottle), will never spontaneously decrease in entropy. It will remain unchanged or move to higher entropy. Therefore, entropy change is about the dispersal of energy, in the form of matter or thermal energy, as shown in Interactive Figure 20.1.3. Here are some statements of the second law using the concept of entropy: ● All physical and chemical changes occur such that the total entropy of the universe increases. uni2206 S universe 5 uni2206 S system 1 uni2206 S surroundings 7 0 for a spontaneous process (20.1) ● The entropy of an isolated system never spontaneously decreases. uni2206 S isolated $ 0 Note that the entropy of a system could go down, provided that the entropy of the sur-roundings goes up more, or visa versa, so that the sum of the changes is greater than zero. The underlying message is that for an exchange of energy to occur spontaneously, some of the energy must become more diffuse. The consequence is that some energy must always be discarded as heat. Other ways to say this include: ● It is impossible to completely turn heat (diffuse energy) into work (concentrated energy).
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
The Cla usius equation of δ q rev / T = Δ S introduces the measurement of entropy change, Δ S . Entropy change describes the direction and quantifies the magnitude of simple changes such as heat transfer between systems – always from hotter to cooler spontaneously. The thermodynamic entropy therefore has the dimension of energy divided by temperature, and the unit joule per kelvin (J/K) in the International System of Units (SI). Thermodynamic entropy is an extensive property, meaning that it scales with the size or extent of a system. In many processes it is useful to specify the entropy as an intensive property independent of the size, as a specific entropy characteristic of the type of system studied. Specific entropy may be expressed relative to a unit of mass, typically the kilogram (unit: Jkg -1 K -1 ). Alternatively, in chemistry, it is also referred to one mole of substance, in which case it is called the molar entropy with a unit of Jmol -1 K -1 . Thus, when one mole of substance at 0K is warmed by its surroundings to 298K, the sum of the incremental values of q rev / T constitute each element's or compound's standard molar entropy, a fundamental physical property and an indicator of the amount of energy stored by a substance at 298K. Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture. Entropy is equally essential in predicting the extent and direction of complex chemical reactions. For such applications, Δ S must be incorporated in an expression that includes bo th the system and its surroundings, Δ S universe = Δ S surroundings + Δ S system . This expression becomes, via some steps, the Gibbs free energy equation for reactants and products in the system: Δ G [the Gibbs free energy change of the system] = Δ H [the enthalp y change] − T Δ S [the entropy change]. Entropy change When an ideal gas undergoes a change, its entropy may also change.
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- 2014(Publication Date)
- Academic Studio(Publisher)
Thermodynamic entropy is a non-conserved state function that is of great importance in the sciences of physics and chemistry. Historically, the concept of entropy evolved in order to explain why some processes are spontaneous and others are not; systems tend to progress in the direction of increasing entropy. Entropy is as such a function of a system's tendency towards spontaneous change. For isolated systems, entropy never decreases. This fact has several important consequences in science: first, it prohibits perpetual motion machines; and second, it suggests an arrow of time. Increases in entropy correspond to irreversible changes in a system, because some energy must be expended as waste heat, limiting the amount of work a system can do. In statistical mechanics, entropy is essentially a measure of the number of ways in which a system may be arranged, often taken to be a measure of disorder (the higher the entropy, the higher the disorder). Specifically, this definition describes the entropy as being proportional to the logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system (microstates) which could give rise to the observed macroscopic state (macrostate) of the system. The constant of proportionality is the Boltzmann constant. The second law of thermodynamics The second law of thermodynamics states that in general the total entropy of any system will not decrease other than by increasing the entropy of some other system. Hence, in a system isolated from its environment, the entropy of that system will tend not to decrease. It follows that heat will not flow from a colder body to a hotter body without the application of work (the imposition of order) to the colder body. Secondly, it is impossible for any device operating on a cycle to produce net work from a single temperature reservoir; the production of net work requires flow of heat from a hotter reservoir to a colder reservoir.
eBook - PDF- Sigurd Skogestad(Author)
- 2008(Publication Date)
- CRC Press(Publisher)
For a perfect crystal at O K, there is only one way to arrange the atoms so that the entropy (“degree of disorder”) in this state can be set to zero. The third law implies that it is meaningful to assign an absolute value for the entropy of each component (where S = 0 for the component as a perfect crystal at 0 K). Nevertheless, since we in this book are only interested in entropy changes, we normally do not use this; instead we (somewhat arbitrarily) set S = 0 for the elements in their standard state at 298.15 K and 1 bar. 7.2 Calculation of entropy The entropy of a system can, as mentioned above, be theoretically calculated from statistical mechanics by considering the probability of the system’s state on the microscopic level. From this, it is clear that the entropy is a state function. How can we compute changes in the system’s entropy by considering changes at the macroscopic level? Well, since we know that entropy is a state function, let us consider a reversible process. How can the entropy (“degree of disorder”) change for such a system? It can not be caused by internal processes, since these are assumed to be reversible. Entropy changes must therefore be caused by interactions with the surroundings, which for a closed system involves transfer of work W and heat Q . Now, work is by definition “organized energy transfer” so this does not change the disorder (entropy). Thus, the only remaining source of change in disorder is the heat transfer Q , which is “disorganized” energy transfer and thus involves a transfer of disorder (entropy). Thus, we have for a reversible process that the only way to increase the system’s entropy is by supplying heat Q . However, by how much does the entropy increase (quantitatively)? Intuitively, the increase in disorder (entropy) for a given Q is larger when the system temperature T is low. This intuition is correct, and it turns out that the entropy increase is given by Q/T .
eBook - PDF- Lokesh Pandey(Author)
- 2020(Publication Date)
- Arcler Press(Publisher)
Alternately, entropy is the physical property of the body that remains constant in an adiabatic process. Entropy is a measure of the part that cannot be used to do work. So, entropy is useful in that it provides the information regarding structural changes accompanying a given process. In a way, entropy is useful for knowing the efficiency of the internal energy of something. Entropy is very significant in thermodynamics. The significances are mentioned below: • Entropy is a physical quantity. It is equal to the ratio of heat absorbed or rejected to the temperature; • It indicates the direction of heat flow; • It helps in determining the thermodynamic state of an object; • Like temperature, pressure, volume, internal energy, magnetic behavior it expresses the state of a body; • The orderliness of an object decreases with the increase of entropy; and • Like temperature or pressure, it cannot be felt. Entropy is the measure of the disorder or randomness in a system. In other words, if you drop a box of matches on the floor, the matches will fall all over the place, which is an increase in entropy. It has been seen that entropy shows an elusive nature. The elusive nature depicted by entropy may be catered to the elusive nature of heat and the motion of the material structure which is related to it. The motion of the material structure is also coupled to the thermal energy through the conversion of the other energy types to heat, in addition to the thermal processes. The unique form and the distinctiveness of entropy along with the nature of entropy to be universally applicable, derive from the fact that all the processes that take place in the universe in the surroundings at all the points of time and space, happen due to the displacement of mass and energy which has been forced.
eBook - PDFAn Introduction to Chemical Metallurgy
International Series on Materials Science and Technology
- R. H. Parker, D. W. Hopkins(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
CHAPTER 2 Entropy y Free Energy and Chemical Equilibrium 2.1. Introduction In the first chapter, we were mainly concerned with an experimental law—the First Law of Thermodynamics—and its implications. In this chapter we shall again be considering the results of experiment, and these can be introduced by the following facts, which are both statements of the Second Law of Thermodynamics: (i) heat always flows from a hotter to a colder body—never in the reverse direction; (ii) an isolated system always tends to take up a more disordered form—never of its own accord becoming more ordered. We would be surprised to find that if two ingots—one at 100°C and the other at 500°C—were placed close to one another in a soaking pit with no other source of heat, the hotter ingot increased in temperature until it melted, whereas the colder ingot cooled down to 0°C. Instead, the temperature of the hotter ingot would always decrease as heat flowed out from it (whether by radiation, convection or conduction) to raise the temperature of the colder ingot. If we consider a pattern formed by coloured counters on a flat board (Fig. 2. la), we know that if the counters were picked up and thrown down again, they would form a pattern of the type shown in Fig. 2.1b. We say that the counters in (a) are more ordered than those in (b). If the counters in (b) were 38 ENTROPY, FREE ENERGY 39 picked up and thrown down again it would be very improbable that they would fall in the pattern (a). We know that state (b) is more probable than state (a), and can calculate, by the techniques of statistics, the probability W of the two systems. We know that W{ h ) > W( a ), and it is an experimental fact that, in any change which is dependent only on the laws of chance, the change will be such that the probability of the state of the system will increase. A more disordered system is more probable than a more ordered system, so that changes of this type are accompanied by an increase in disorder of the system.
- Elias I. Franses(Author)
- 2014(Publication Date)
- Cambridge University Press(Publisher)
It is indeed remarkable that, if one has such data, then no new data are required in order to “ measure ” or determine the values of entropies. Once entropy values of initial and fi nal states have been calculated, one can determine from these values whether any process can occur spontaneously or cannot occur at all, as will be shown in Section 7.11 . If we integrate Eq. (7.43) from an initial state A to a fi nal state B, we get Δ S ¼ S ð state B Þ − S ð state A Þ ¼ ð B A d Q rev T : ð 7 : 44 Þ If we call state A the “ reference state, ” and we arbitrarily assign its entropy as S 0 , then we can calculate the entropy of any other state B as S ð B Þ ¼ S 0 þ ð B 0 d Q rev T : ð 7 : 45 Þ 200 The Second Law, absolute temperature, … Thus, in the context of the Second Law only the relative, and not the absolute, entropy can be de fi ned and calculated. This is similar to the calculation of the relative internal energy (and the relative enthalpy), which can be done on the basis of the First Law (see Section 4.1 ). The absolute internal energy cannot be calculated from macroscopic thermodynamic principles. The absolute entropy can be calculated only after an additional macroscopic thermo-dynamic principle, the “ Third Law, ” has been introduced. According to that principle, the entropy at the limit of the absolute temperature T at 0 K, or T 0 K, or T ! 0 K, is zero. The molecular interpretations of entropy, “ zero entropy, ” and absolute entropy are discussed in Chapter 14 . Now we need to develop methods for calculating relative entropies, or calculating the values of the de fi nite integral in Eq. (7.45) . We will fi rst cover several simple examples such as the expansion of an ideal gas, the heating of a liquid, and a heat transfer process. Then we will cover a completely general method of determining relative entropies from data.
eBook - PDF- Claus Borgnakke, Richard E. Sonntag(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
In fact, the question “What is entropy?” is frequently raised by students, with the implication that no one really knows! This section has been included in an attempt to give insight into the qualitative and philosophical aspects of the concept of entropy and to illustrate the broad application of entropy to many different disciplines. First, we recall that the concept of energy arises from the first law of thermodynamics and the concept of entropy from the second law of thermodynamics. Actually, it is just as difficult to answer the question “What is energy?” as it is to answer the question “What is entropy?” However, since we regularly use the term energy and are able to relate this term to phenomena that we observe every day, the word energy has a definite meaning to us and thus serves as an effective vehicle for thought and communication. The word entropy could serve in the same capacity. If, when we observed a highly irreversible process (such as cooling coffee by placing an ice cube in it), we said, “That surely increases the entropy,” we would soon be as familiar with the word entropy as we are with the word energy. In many cases, when we speak about higher efficiency, we are actually speaking about accomplishing a given objective with a smaller total increase in entropy. A second point to be made regarding entropy is that in statistical thermodynamics, the property entropy is defined in terms of probability. Although this topic will not be exam- ined in detail in this book, a few brief remarks regarding entropy and probability may prove helpful. From this point of view, the net increase in entropy that occurs during an irreversible process can be associated with a change of state from a less probable state to a more probable state. For instance, to use a previous example, one is more likely to find gas on both sides of the ruptured membrane in Fig. 5.15 than to find a gas on one side and a vacuum on the other.
eBook - PDFChemistry
An Atoms First Approach
- Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
However, we can assign absolute entropy values. Consider a solid at 0 K, where molecular motion virtually ceases. If the substance is a perfect crystal, its internal ar- rangement is absolutely regular [Fig. 16.5(a)]. There is only one way to achieve this perfect order: Every particle must be in its place. For example, with N coins there is only one way to achieve the state of all heads. Thus a perfect crystal represents the lowest possible entropy; that is, the entropy of a perfect crystal at 0 K is zero. This is a statement of the third law of thermodynamics. As the temperature of a perfect crystal is increased, the random vibrational mo- tions increase, and disorder increases within the crystal [Fig. 16.5(b)]. Thus the en- tropy of a substance increases with temperature. Since S is zero for a perfect crystal at 0 K, the entropy value for a substance at a particular temperature can be calculated by knowing the temperature dependence of entropy. (We will not show such calcula- tions here.) The standard entropy values (S8) of many common substances at 298 K and 1 atm are listed in Appendix 4. From these values you will see that the entropy of a substance does indeed increase in going from solid to liquid to gas. One especially interesting feature of this table is the very low S8 value for diamond. The structure of diamond is highly ordered, with each carbon strongly bound to a tetrahedral ar- rangement of four other carbon atoms (see Section 9.7). This type of structure al- lows very little disorder and has a very low entropy, even at 298 K. Graphite has a slightly higher entropy because its layered structure allows for a little more disorder.
- Christof M. Aegerter(Author)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
Left Right Total number of possibilities Total Fraction L R 6.25% 25.00% 37.50% 25.00% 6.25% 100.00% 16 1 4 6 4 4 1 0 3 3 3 3 2 2 2 2 2 2 0 Figure 8.10 Illustration of probability interpretation of entropy. Randomly distributed particles in a container with two halves are distributed with greater frequency equally. For many particles, the likelihood that all the particles in a half are extremely strong decreases. 339 Entropy and the Laws of Thermodynamics So we can reinterpret the second law of thermodynamics, i.e., that entropy always increases with irreversible processes, to a statement that such processes always go in the direction of a more probable state. From this consideration of the probability of a macroscopic state that can arise from many random processes, we can also make plausible the Boltzmann distribution, which we found earlier. The probability of a state is given exactly by e to the power of the entropy divided by k B : P ∝ exp(S/k B ). This directly results in the Boltzmann distribution P ∝ exp(−E/(k B T)) if we remember the link between entropy and heat as well as the first law of thermodynamics. If we want to change the entropy, that is, to change the probabilities of the microscopic states, we must do work on the system. The Boltzmann distribution tells us how these probabilities and the work are related. That is, processes in which the entropy is changed (or the entropy multiplied by the temperature) give a force countering the macroscopic force that performs this macroscopic work. If we consider the previous example of a gas enclosed in a vessel and decrease its volume using a piston, the microscopic probabilities change. The (infinitesimal) change in entropy then is dS = Nk B ln((V + dV)/V), where N is the number of particles and V is the volume, which changes by the small amount dV. For small changes, we can Taylor-expand the logarithm and obtain the work that is to be done: dW = TdS = Nk B TdV/V.
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