Absolute scale of entropy

Absolute Scale of Entropies. Absolute Standard Entropy, 98K... 

Planck s statement of the Third law suggests that a scale for the absolute value of entropy can be set up ... 

The work of Carnot, published in 1824, and later the work of Clausius (1850) and Kelvin (1851), advanced the formulation of the properties of entropy and temperature and the second law. Clausius introduced the word entropy in 1865. The first law expresses the qualitative equivalence of heat and work as well as the conservation of energy. The second law is a qualitative statement on the accessibility of energy and the direction of progress of real processes. For example, the efficiency of a reversible engine is a function of temperature only, and efficiency cannot exceed unity. These statements are the results of the first and second laws, and can be used to define an absolute scale of temperature that is independent of ary material properties used to measure it. A quantitative description of the second law emerges by determining entropy and entropy production in irreversible processes. 

The traditional way to approach the subject is to state the Second Law as it has been deduced on the basis of years of experience, and then show through use of the Carnot cycle the logical consequences (such as the existence of the entropy and an absolute scale of temperature). Two logically equivalent ways of stating the Second Law are... 

The second law is concerned with changes in entropy (AS). The third law of thermodynamics provides an absolute scale of values for entropy by stating that for changes involving only perfect crystalline solids at absolute zero, the change of the total entropy is zero. This law enables absolute values to be stated for entropies. 

For the enthalpies, we have also managed to assign to each compound a standard enthalpy by the standard enthalpies of formation, by arbitrarily giving the value of zero to the enthalpy of formation of the simple substances at any temperature. In the case of entropies, we shall construct a scale by deciding that for all solid substances, the entropy has the same value at a certain temperature. Thus, we shall define an absolute scale of the entropies. 

The definition of EPH for the electrode reaction given by Eq. (7) or Eq. (8) is all similar to that of a cell reaction except on the absolute scale. These equations indicate that EPH of a halfcell, just like that of the cell reaction, is also a characteristic quantity that only relates to changes in the function of state, i.e. the entropies on the absolute scale, of substances taking part in the reaction. The heat effect occurs on the electrode-electrolyte interfaces. Evidently, when Eq. (7) or Eq.(8) is apphed to a cell reaction, the terms, (H /H2) in Eq. (5), common to both electrodes of the cell, does not appear exphdtly because they are deleted ultimately. 

Now we know that electrode potential is a thermodynamic value. Thus, as any thermodynamic characteristics (except for entropy), it can be determined with an accuracy up to some arbitrary constant. However, in the early years of electrochemical science, there were many attempts to define an absolute scale of the electrode potentials. 

It is noteworthy that a statistical mechanical calculation of absolute values of entropy or free energy is not required for determination of thermodynamic properties of matter. The functional dependence of the partition function on macroscopic properties, such as the total mass, volume, and temperature of the system, is sufficient to derive equations of state, internal energies, and heat capacities. For example, knowledge that the ideal gas partition function scales as is adequate to define and explain the ideal gas equation of state. 

We have therefore used the Third Law of Thermodynamics to define absolute zero for a scale of standard entropy, thus ... 

When the pressure/ is expressed in atmospheres, then at the boiling point 7 the pressure/ = i and thus C R = AHjTb = AS. In this last expression we meet the latent heat of evaporation at constant pressure, divided by the boiling point temperature on the absolute scale according to Trouton s rule this quotient has an approximately constant value actually about 22 for normal liquids. This means, therefore, that the entropy of evaporation (at i atm.) also amounts approximately to 22 cal/mole degree (alkali halides 24 cal/mole degree). 

In the classical formulation, the second law of thermodynamics states that there exist an absolute scale for the temperature T and an extensive function 5(p, V, called the entropy, such that for an infinitesimal process in a closed system... 

The individual molar entropies under standard conditions of the various participating species are generally available in tabular form these are determined as shown in Section 1.17. Alternatively, they are found via an empirical equation of state, as in Eqs. (1.13.10), (1.13.12), followed by an integration the temperature of the reaction is a parameter. As explained in Section 1.17, if nuclear effects may be excluded, or any frozen-in disorder remains undisturbed (or any nonequi-libreated condition is not altered), one may set the entropy of all participants in the reaction, whether they be elements or compounds, equal to zero at T = 0. This then establishes an absolute scale for the tabulated entropies of the reagents and products at any temperature T. The reader is asked to set up strategies for determining ASt,kx for reactions under other than standard conditions see Exercise 3.9.7. As an example one may cite the reaction... 

Provisionally T will be identified with the temperature on the ideal gas scale. By assuming the above property as a definition of the absolute scale, a crucial experiment can be devised (Joule and Thomson, 1862) which exactly verifies this conclusion. If a standard entropy, under chosen conditions, is lenoted by 5° then the entropy is generally... 

Some actual experimental data will be quoted below (sec Table XVI), but for the present sufficient indication has been given of the procedure used for determining the entropies of substances which are solid or liquid at ordinary temperatures. For such substances the standard states are the pure solid or pure liquid at 1 atm. pressure (cf. 12e), and the standard entropies, per g. atom (for elements) or per mole (for compounds), at 25 C, derived from heat capacity measurements are recorded in Table XV. As stated earlier ( 19h), entropies are usually expressed in terms of calories per degree, and the quantity 1 cal. deg. the temperature being on the usual absolute scale, in terms of the centigrade degree, is often referred to as an entropy unit and abbreviated to e.u. 

These parameters can be displayed as a volume profile for a reaction to complement other thermodynamic parameter profiles of free energy, enthalpy and entropy. It is also possible in certain circumstances, discussed below, to place the volume profile on an absolute scale rather than only on a relative volume scale. 

Entropy, alone among the thermodynamic functions, is therefore measured on an absolute scale having the reference point zero at 0 K for pure, perfectly crystalline materials. As we shall see, the other functions (G, H, A, U) are measured against an arbitrary standard state and are assigned relative, rather than absolute values. (That is why entropy is designated by an absolute symbol, S°, and all others by relative symbols, e.g., AjG°, in thermochemical tables, as we shall see in Chapter 7). Apart from this, most of thermodynamics as presented here would survive intact if the Third Law had never been discovered. 

This is based upon the so-called triple point of water, where all three states of aggregation (ice, water, water vapor) coexist and where pressure can be ignored. [When water is at the triple point, the pressure is fixed (see Sect. 11.5).] This odd numerical value is chosen so that the temperature difference between the normal freezing and boiling points of water is close to 100 units, as it is in the Celsius scale. For this reason, one Kelvin is one 273.16th of the thermodynamic temperature of the triple point of water. The zero point of the Kelvin scale lies at the absolute zero point which is indicated by an absence of entropy in the body. When one wishes to establish the relation between thermodynamic temperature T and Celsius temperature 5, it is important to be careful to set the zero point of the Celsius scale to the freezing point of water at normal pressure. This lies nearly exactly 0.01 K under the temperature of water s triple point, so that ... 

The equations we have developed up to this point can be used to calculate differences in enthalpy and entropy between states. To calculate absolute values we must also know the actual value of enthalpy and entropy at some state. This actual value, however, is not important if our ultimate interest is in calculating differences. Indeed, in all problems of practical interest, this will be the case. And yet, it is convenient to calculate properties on absolute scale, as the steam tables demonstrate, because then differences can be calculated simply as algebraic differences between the values of a property at two states. Absolute properties are really differences from a state that we accept as a reference. This is common practice for many physical quantities, including potential energy, elevation, even kinetic energy. To the extent that the choice of the reference does not affect differences, reference states maybe chosen arbitrarily. With respect to enthalpy and entropy, the choice is usually made so as to simplify the overall calculation. 

ArG298 = -RT InK. This experimental scale of relative acidities was converted to a scale of absolute acidities by including certain compounds as anchor points. Thus, the gas-phase acidity of PH3 was determined to be ArG29s = 363 2 kcal/mol. The entropy change for the deprotonation process was evaluated by procedures using statistical mechanics as ArS = 24.9 2 cal - mol" K From these data the deprotonation enthalpy of PH3 at 298 K was calculated to be ArH298=PA(PHi) = 370.4 2 kcal/mol [1, 2]. 

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