Third Law of Thermodynamics

12 Key excerpts on "Third Law of Thermodynamics"

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  eBook - ePub

  Practical Chemical Thermodynamics for Geoscientists

  • Bruce Fegley Jr., Bruce Fegley, Jr.(Authors)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  Chapter 9

  The Third Law of Thermodynamics

  If the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature: every substance has a finite positive entropy, but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances.

  —Lewis and Randall (1923)

  The Third Law of Thermodynamics is the subject of this chapter. The third law is important because it states that entropy is an absolute quantity that can be determined from calorimetric measurements of the heat capacity and enthalpies of transition of a material such as forsterite. We can thus compute the Gibbs free energy of a chemical reaction using only thermochemical data (the absolute entropies and standard enthalpies of formation for reactants and products).

  There are four sections in this chapter. Section I describes the historical development of the Nernst heat theorem, which is the forerunner of the Third Law of Thermodynamics. Section II states the third law and examines some of its important consequences. Section III discusses the third law and entropy and describes the different contributions to the total entropy of a material. Section IV discusses calculation of absolute entropies from heat capacity data, introduces the Gibbs function [(

  GT o

  – H 298 o )/T ], and describes the use of the third law for computing Gibbs free energies of reaction from calorimetric data.

  I Historical Development of the Nernst Heat Theorem

  During the latter half of the 19th century, chemists began to use the first and second laws of thermodynamics in their research. They wanted to predict the direction and driving force of chemical reactions and the extent to which different reactions would occur. Once this information was available for a particular reaction, the optimal pressure and temperature could be used to maximize the amount of a desired product. One example is the synthesis of ammonia, which is essential for production of synthetic fertilizers to increase agricultural production. Initially, chemists thought that the enthalpy of reaction could be used to predict which reactions would occur. Everyday experience showed that many spontaneous reactions, such as coal burning in air, acids dissolving in water, metals dissolving in acids, or explosions, produced heat. Thus, the French chemist Marcellin Berthelot and the Danish chemist Julius Thomsen undertook extensive measurements of the heats of formation for thousands of substances (see their biographical sidebars in Chapter 5 ). In the 1850s, Thomsen proposed that all spontaneous reactions generate heat. In the 1860s, Berthelot proposed a similar concept, the principle of maximum work

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  Thermodynamics

  • H J Kreuzer, Isaac Tamblyn;;;(Authors)
  • 2010(Publication Date)
  • WSPC

    (Publisher)

  Although a concept of great appeal for science fiction one must be cautious simply be-cause the universe is not just a closed system; it might be but we do not know. In any case, the time scale for this to happen is enormous provided the universe does not collapse back onto itself as some cosmologists believe. Remark 3.9. Robert Emden, whom we will meet again in Section 7.3.5, circumscribed the roles of energy and entropy in a rather poetic way: “ In the huge manufactory of natural processes, the principle of entropy occu-pies the position of manager, for it dictates the manner and method of the whole business, whilst the principle of energy merely does the book-keeping, balancing credits and debits. ” 3.6 Third law or Nernst’s theorem: Zero temperature can-not be attained We begin historically with Nernst’s theorem, which he stated as lim T → 0 Δ S = 0 (3.3) This implies that as we lower temperature, we must isolate the system completely from the surrounding world to avoid even the smallest transfer of heat (which would raise the temperature again). Thus, in the quest for absolute zero, experiments become increasingly more complicated and expensive. To restate this in the form of a law, Zero temperature cannot be attained. This is the second formulation of the Third law, also attributable to Nernst, and is equivalent in its content to (3.3). The Laws of Thermodynamics 51 Note that absolute zero means there are no thermal effects in our system, and thermodynamics “reduces” in its content to classical mechanics, or, ultimately, quantum mechanics. Both of these theories are deterministic and give you complete knowledge about the behavior of a system. Thus zero temperature implies zero disorder, which means zero entropy. In classical mechanics, the idea of a system with only conservative forces, i.e. no frictional forces, cannot be achieved completely.

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  eBook - ePub

  Physical Chemistry

  How Chemistry Works

  • Kurt W. Kolasinski(Author)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  Third Law of Thermodynamics:

  The entropy of a pure, perfectly crystalline substance is zero at 0 K.

  Mathematically, this was stated by Planck as

  The entropy of any system vanishes in the state for which

  (9.59)

  The advantage of this formulation is that it allows us to calculate absolute molar entropies. It also facilitates the calculation of equilibrium constants solely on the basis of thermochemical measurements. We need to specify that the system is at internal equilibrium because it is possible for a system to get trapped into a long-lived nonequilibrium state. One example of such is a glass. Hence, the Planck formulation specifies a crystalline substance rather than a solid of any form. Nuclear spin interactions in the absence of a magnetic field produce extremely weak interactions. So weak, in fact, that the energy level spacing is still significantly smaller than thermal energy even at 1 K. Randomly oriented nuclear spins can induce significant disorder that does not relax until the temperature is well below 1 K.

  9.8 The unattainability of absolute zero

  Consideration of the limits of the universe can lead to consideration of our limits to consider. Thus, we are left to ponder a consequence of the Third Law that some consider to be a statement of the Third Law:

  A state with a temperature of absolute zero is unattainable through any process composed of a finite number of steps.

  Conceptually, we can argue this way. To lower the temperature of a system by an amount dT, we need to extract an amount of heat dq. We know the relationship between these two variables is given by dq = C dT

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  Thermodynamics with Chemical Engineering Applications

  • Elias I. Franses(Author)
  • 2014(Publication Date)
  • Cambridge University Press

    (Publisher)

  14 The Third Law and the molecular basis of the Second and Third Laws 14.1 INTRODUCTION ................................................................................................. So far, we have covered fi ve new basic principles (axioms or postulates) of thermodynamics, in addition to the two principles of mechanics (mass conservation and Newton ’ s second law of motion). These principles are the following: (a) the existence of an equilibrium phase, or the “ Minus Second Law, ” see Chapter 3 ; (b) the existence of an equation of state for each thermodynamic phase, or the “ Minus First Law, ” see Chapter 3 ; (c) the existence of the empirical temperature θ as a function of state, associated with the “ Zeroth Law, ” see Chapter 3 ; (d) the existence of the internal energy U as a function of state, and the heat Q as a path-dependent function, and the expanded energy conservation principle, all associ-ated with the “ First Law, ” see Chapter 4 ; and (e) the existence of the absolute thermodynamic temperature T and of the entropy S , as state functions, and the principle of entropy inequality, all associated with the “ Second Law, ” see Chapter 7 . For any physical or chemical process to be possible, the mass and energy conservation principles and the entropy inequality principles must be satis fi ed. In the above principles the energy ( U or E k or E p ) is de fi ned on a relative basis, not on an absolute basis, relative to an arbitrary value of energy at a reference state. The internal energy has a clear molecular basis. It is the combined kinetic energy and potential energy of the individual molecules comprising a given phase or system. The absolute temperature T is a measure of the average kinetic energy of the molecules. The entropy is also de fi ned on a relative basis, using the Second Law.

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  Thermodynamics and Statistical Mechanics

  An Integrated Approach

  • M. Scott Shell(Author)
  • 2015(Publication Date)
  • Cambridge University Press

    (Publisher)

  311 15.3 Entropy differences at absolute zero 15.4 Attainability of absolute zero So far we have considered the third law in relation to the existence of molecules. Such was also the case when we initially examined the first and second laws. However, we eventually found that those laws could also be formulated at a purely macroscopic level: we could think of the first law in terms of heat and work rather than constant-energy Newtonian mechanics, and we could define the entropy in terms of reversible heat transfers dS ¼ δQ rev /T rather than microstates. It therefore may come as no surprise that the third law also has a purely macroscopic formulation. A third formulation of the Third Law of Thermodynamics states that the temperature absolute zero is unattainable in any process with a finite number of steps and in finite time. This form of the law was also proposed by Nernst as an alternative to his earlier theorem and is arguably one of its most general presentations. Indeed, no reference to the molecular world is required and this statement can be directly tested by experiments; countless experimental efforts support the unattainability of absolute zero. Some view this presentation of the third law as the most fundamental, requiring the least qualifications. There is a close connection between the unattainability statement and the mole- cular quantum picture. We first need to specify what we mean by attainability. In order to reach absolute zero, ultimately we must perform some kind of isentropic process such as a reversible adiabatic expansion that accomplishes cooling. Or, the process could be more complicated and consist of a combination of isentropic and isothermal steps, so long as the last step is isentropic. The final step can never be isothermal because that would presume the availability of a heat reservoir already 0 0 superfluid crystal normal liquid Figure 15.2.

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  Physical Chemistry An Advanced Treatise

  • Wilhelm Jost(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  For example, Fig. 19 shows a schematic entropy-temperature diagram in which only entropy differences tend to zero; no finite number of pro-cesses such as ABC can lead to absolute zero. At first sight, the result that entropy differences should vanish appears significantly different from the statement that the entropy of each aspect should vanish. In fact, as we discussed in Section V, the point is of little importance, as each statement leads to the same practical consequences. It is sometimes claimed that the unattainability formulation of the third law is preferable to that given previously, as it provides a precise statement of the law without any qualifying clause concerning the condi-tion of internal equilibrium. That is, it states that absolute zero is unattain-able, independent of whether or not the system is in internal equilibrium. In fact, the unattainability formulation offers little advantage. We have seen that one of the main applications of the law is to indicate whether the solid phase of a system is in internal equilibrium. Therefore, the con-cept of internal equilibrium must always be borne in mind when apply-ing the third law, and this is best achieved by the standard formulation. (11.6) (11.7) S «(0) > SK(0). 6. T h e T h i r d L a w of T h e r m o d y n a m i c s 483 T F I G . 1 9 . Schematic entropy diagram of a system in which the entropy does not vanish, b u t in which absolute zero is unobtainable. D . T H E L O W E S T T E M P E R A T U R E S T h e third law implies that we can never attain the temperature of absolute zero. We now briefly consider to what extent this limitation restricts experimental work at low temperatures. The method of reaching the lowest temperatures involves the adiabatic demagnetization of magnetic material, whose entropy depends on both temperature and magnetic field. # Figure 20 shows an entropy-tempera-ture curve of a typical paramagnetic salt used to obtain temperatures below 1°K.

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  eBook - ePub

  Chemical Thermodynamics: Principles and Applications

  Principles and Applications

  • J. Bevan Ott, Juliana Boerio-Goates(Authors)
  • 2000(Publication Date)
  • Academic Press

    (Publisher)

  Chapter 4

  The Third Law and Absolute Entropy Measurements

  In the previous chapter, we saw that entropy is the subject of the Second Law of Thermodynamics, and that the Second Law enabled us to calculate changes in entropy ΔS . Another important generalization concerning entropy is known as the Third Law of Thermodynamics . It states that:

  Every substance has a finite positive entropy, but at the absolute zero of temperature the entropy may become zero, and does so become in the case of a perfect crystalline substance .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 ordereda 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 .

  To obtain S , we start with equation (3.15) from the previous chapter

  (3.15)

  Separating variables and integrating gives

  (4.1)

  According to the Third Law, S 0 = 0 and equation (4.1) becomes

  (4.2)

  Equation (4.2) can be used to determine the entropy of a substance. A pure crystalline sample is placed in a cryogenic calorimeter and cooled to low temperatures. Increments of heat, q , are added and the temperature change, ΔT , is measured, from which the heat capacity can be calculated from the relationship

  (4.3)

  Equation (4.3) is exactly true only if q is an infinitesimal amount of heat, causing an infinitesimal temperature rise, dT . However, unless the heat capacity is increasing rapidly and nonlinearly with temperature, equation (4.3) gives an accurate value for

  Cp

  at the average temperature of the measurement.c Continued addition of heat gives the heat capacity as a function of temperature. The results of such measurements for glucose are shown in Figure 4.1 .2

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  Thermodynamics of the Earth and Planets

  • Alberto Patiño Douce(Author)
  • 2011(Publication Date)
  • Cambridge University Press

    (Publisher)

  But the direction of a spontaneous change in a crystal that is not an isolated system (which is the common situation in nature) is not necessarily determined by an increase in entropy, but rather by a decrease in the thermodynamic potential appropriate to the constraints on the system. We return to this in Sections 4.8 and 4.9. 206 The Second Law of Thermodynamics 4.7 The Third Law of Thermodynamics 4.7.1 Statement of the Third Law of Thermodynamics There is an additional principle, called the Third Law of Thermodynamics, that is inde- pendent of the First and Second Laws. It is essential in the development of chemical thermodynamics, although much of classical thermodynamics and its applications to heat engines and other engineering processes do not require it. We introduce the Third Law by stating that experimental evidence shows that, as temperature approaches 0 K, heat capacities (C P and C V ) approach zero faster than temperature, i.e.: lim T →0  C P T  = 0. (4.65) A few examples are shown in Fig. 4.8. A consequence of (4.65) is that the entropy difference of a substance between 0 K and any other temperature, T, is a finite value. Assuming that heating takes place at constant pressure, and that there are no phase transitions between 0 and T, then dQ = C p dT , and we have: S (T ) − S (0) =  T 0 d S =  T 0 C P T dT (4.66) with condition (4.65) guaranteeing that the integral does not blow up. An unknown integration constant remains, however, which is the entropy at 0 K. 0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 T (K) C P / T (JK –2 mol –1 ) K Cl Enstatite MgO Fig. 4.8 Low temperature behaviors of C P /T for an ionic crystal (KCl, data from Berg & Morrison, 1957), a crystalline oxide (MgO, data from Barron et al., 1959) and a crystalline silicate (enstatite, data from Krupka et al., 1985).

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  Introduction to the Thermodynamics of Materials

  • David R. Gaskell, David E. Laughlin(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  3 The Second Law of Thermodynamics 3.1INTRODUCTION

  In Chapter 2 , it was seen that when a system undergoes a change of state, the consequent change in the internal energy of the system is dependent only on the initial and final states and is equal to the algebraic sum of the thermal energy, q , and work, w , effects. Two questions now arise.

  1.What magnitudes may the q and w effects have?

  2.What criteria govern these magnitudes? Two extreme cases related to the first question can occur.

  •w = 0 and q = ∆U′

  •q = 0 and w = –∆U′

  But if q ≠ 0 and w ≠ 0, a third question arises.

  3.Is there a definite limit to the amount of work which the system can do during its change of state?

  The answers to these questions require an examination of the nature of the processes which affect q and w . This examination, which is made in this chapter, identifies two types of processes (reversible and irreversible processes) and introduces a state function called the entropy (S ).

  The concept of entropy will be introduced from two different starting points. In Sections 3.2 through 3.8, entropy will be seen as a quantification of the degree of irreversibility of a process. In Sections 3.10 through 3.14, it will be seen that, as a result of an examination of the properties of reversibly operated heat engines, there naturally develops a quantity which has all the properties of a thermodynamic state function. This state function is the entropy. These findings lead to a statement of the Second Law of Thermodynamics, which, together with the other laws of thermodynamics lay the foundation for the thermodynamic method of describing the behavior of matter to be discussed in the text.

  3.2SPONTANEOUS OR NATURAL PROCESSES

  A system left to itself will do one of two things: it may remain in the state in which it happens to be or it may change of its own accord to some other state. That is, if the system is initially in equilibrium with its surroundings, then, left to itself, it will remain in this equilibrium state. On the other hand, if the initial state is not the equilibrium state, the system will spontaneously* (i.e., without any external influence) move toward its equilibrium state. The equilibrium state is a state of rest (at least at the macroscopic level), and thus, once at equilibrium, a system will only move away from equilibrium if it is acted on by some external agency. Even then, the combined system, comprising the original system and the external agency, is simply moving toward the equilibrium state of the new combined system. A process which involves the spontaneous movement of a system from a nonequilibrium state to an equilibrium state is called a natural or spontaneous process. Since such a process cannot be reversed without the application of an external agency which leaves a permanent change in this agency, such a process is said to be irreversible . The terms natural , spontaneous , and irreversible

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  eBook - ePub

  Elementary Chemical Thermodynamics

  • Bruce H. Mahan(Author)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  III

  The Second Law of Thermodynamics

  T HE FIRST LAW of thermodynamics expresses the repeated experimental observation that, while it may be transferred between a system and its surroundings, energy is never created or destroyed. Therefore, we propose that the conservation of energy is a minimum requirement which every real process must satisfy. However, a little reflection shows that naturally occurring processes have a feature which is completely inexplicable on the basis of the first law of thermodynamics. This is best understood by consideration of some simple examples.

  The first example involves the apparatus shown in Fig. 3–1 . Two bulbs are connected by a stopcock; bulb A contains an ideal gas, while bulb B is evacuated. When the stopcock is opened, gas inevitably flows from A to B. It is observed that the system remains at a constant temperature; thus, the process is an isothermal irreversible expansion of an ideal gas. In Chap. 2 we learned that for any isothermal expansion of an ideal gas ΔE = 0. Moreover, there is no mechanical link between our system and its surroundings, so we have w = 0, and consequently q = 0. Despite the fact that the system is not prodded by an interaction with its surroundings, the expansion occurs spontaneously, once the stopcock is opened. Now, the reverse process, in which all the molecules in bulb B spontaneously return to bulb A, would also have q = w =

  E

  = 0, and according to the first law of thermodynamics this would be a perfectly possible occurrence. However, such a spontaneous concentration of the gas in a totally isolated system has never been observed, and consequently we presume it is impossible.

  Figure 3–1 Apparatus for the irreversible expansion of a gas. Bulb A contains the ideal gas; bulb B is initially evacuated.

  There are other instances in which systems change in a predictable way but, left to themselves, never return to their original condition. When two blocks of material, one hot and the other cold, are brought together, the temperature of each block changes until the two reach some uniform intermediate temperature. The flow of heat from the hot to the cold block is spontaneous; it proceeds unaided once the blocks are in contact. On the other hand, two isolated bodies in contact and initially at the same temperature have never been observed to depart from temperature uniformity. In order for them to do so, it would be necessary eventually for heat to flow unaided from a cold body to a hot body. This has never been observed, and we state with some confidence that it can never happen. Yet such a process would certainly not violate the first law of thermodynamics, since the energy lost by the cold body would be exactly equal to that gained by the hot body.

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  Classical and Quantum Thermal Physics

  • R. Prasad(Author)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  A system may be given energy or energy from a system may be withdrawn by carrying out some operation or process on the system. The first law of thermodynamics deals with such situations. The total energy E total of a system may be written as, E total = U T E E E E external Bulk kinetic Bulk Potential any other ( ) + = + ( ) + form of energy 3.15 Thermodynamics: Definitions and the Zeroth Law 107 Energy is measured in terms of the work and, therefore, the units of energy and work are same. The MKS unit of energy is joule (J). Energy may also be expressed in erg, electron volt (eV), kilo watt hour (kWH), British thermal unit (Btu) and calorie (cal). The conversion factors are given below. 1J = I N m; 1 eV = 1.602 × 10 –19 J; 1 erg = 1 × 10 –7 J; 1 cal = 4.1868 J; 1 Btu = 1.0550 × 10 3 J. 3.4 Equilibrium Equilibrium occupies a central place in thermodynamics. A system is said to be in equilibrium if no change in its state functions occur with time. In principle, therefore, it is required to keep the system in observation for infinite time to ensure that no change in system parameters has taken place. Observation of a system for infinite time is possible only in imagination and in practice if system parameter do not change in reasonable time, it is assumed that the system has attained equilibrium. Equilibriums may be of two kinds: (i) natural equilibrium (ii) forced equilibrium or steady state. 3.4.1 Natural equilibrium or equilibrium Any system left to itself for a sufficiently long time attains equilibrium in a natural way. Several examples of natural equilibrium may be given, like hot tea in a cup left for few hours attains the temperature of the surroundings, reaches the state of equilibrium and remains in it for indefinite time without any further efforts. This type of equilibrium, which does not require any effort or energy to maintain equilibrium once it has been attained, is called natural or simply equilibrium.

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  Thermodynamics

  Concepts and Applications

  • Stephen R. Turns(Author)
  • 2006(Publication Date)
  • Cambridge University Press

    (Publisher)

  Imagine the wasted effort of an engineer seeking to improve the thermal efficiency of a power plant to 60% when the second law indicates that 55% is the theoretical maximum achievable. To achieve our goal of quantifying the thermal efficiency of a reversible cycle, we must first define an absolute thermodynamic temperature scale (see item 6 in Table 6.2). 6.4a Kelvin’s Absolute Temperature Scale We have just shown the validity of the statement that, for any engine working between two reservoirs having the same high temperatures and the same low temperatures, a reversible engine will have the greatest thermal efficiency. William Thomson, Lord Kelvin, used this statement to define a temperature scale that is independent of any substance or particular measuring instrument, that is, an absolute temperature scale 5 [8]. We now explore how this was done by mathematically expressing this statement as h rev  f (T H , T L ), (6.11) where f indicates an arbitrary function of the two variables T H and T L . Equation 6.11 implies that the only factors affecting the thermal efficiency of a reversible cycle are the temperatures of the two reservoirs. We combine this second-law conclusion, Eq. 6.11, with the first-law definition of thermal efficiency, Eq. 6.7b, as follows: (6.12) Although there are several choices that can be made for the function f, Kelvin’s choice [9] was to set (6.13a) or (6.13b) Equation 6.13b is then used to create an absolute thermodynamic temperature scale by arbitrarily assigning a numerical value to one of the reservoir temperatures, so that (6.14a) This definition of temperature states that a thermodynamic temperature is directly proportional to the ratio of the heat received by a reversible heat engine at the temperature of interest to the heat rejected at a known fixed T  T fixed a Q T Q T fixed b rev . Q L Q H  T L T H . f (T H , T L )  1  T L T H , h rev  1  Q L Q H  f (T H , T L ).

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