Entropy thermodynamic properties

But a few processes that are endothermic can occur easily. Why Another factor known as entropy can determine if a process will occur. Entropy, S, is a measure of the disorder in a system and is a thermodynamic property. Entropy is not a form of energy and has the units joules per kelvin, J/K. A process is more likely to occur if it is accompanied by an increase in entropy, that is, A5 is positive. 

They can also trace the thematic content of science (von Baeyer 1999) in the formulation of the first and second laws, and see the ways in which entropy defies the expectations of a scientific theory or thermodynamic property. Entropy does not comply with conservation principles and is ever increasing thus it is an awkward fit in a balance equation. Even so, entropy balances abound in undergraduate thermodynamics textbooks (as do entropy inequalities, which students also struggle to understand). 

Thermodynamics rests largely on the consohdation of many observations of nature into two fundamental postulates or laws. Chapter 2 addressed the first law— the energy of the universe is conserved. We camiot prove this statement, but based on over a hundred years of observation, we believe it to be true. In order to use this law quantitatively— that is, to make numerical predictions about a system—we cast it in terms of a thermodynamic property internal energy, u. Likewise, the second law summarizes another set of observations about nature. We will see that to quantify the second law, we need to use a different thermodynamic property entropy, s. Like internal energy, entropy is a conceptual property that allows us to quantify a law of nature and solve engineering problems. This chapter examines the observations on which the second law is based explores how the property s quantifies these observations illustrates ways we can use the second law to make numerical predictions about closed systems, open systems, and thermodynamic cycles and discusses the molecular basis of entropy. 

We would like to generalize our experience with the directionality of nature (and the limits of reversibility) into a quantitative statement that allows us to do calculations and draw conclusions about what is possible, what is not possible, and whether we are close to or far away from the idealization represented by a reversible process. Indeed, it would be nice if we had a thermodynamic property (i.e., a state function) which would help us to quantify directionality, just as internal energy, it, was central in quantifying the conservation of energy (the first law of thermodynamics). It turns out the thermodynamic property entropy, s, allows us to accomplish this goal. 

Gorrespondingly, the thermodynamic property entropy, s, is defined in terms of heat absorbed during a reversible process. In differential form, the change in entropy of a substance undergoing a reversible process is equal to the incremental heat it absorbs divided by the temperature ... 

A quantitative theory of rate processes has been developed on the assumption that the activated state has a characteristic enthalpy, entropy and free energy the concentration of activated molecules may thus be calculated using statistical mechanical methods. Whilst the theory gives a very plausible treatment of very many rate processes, it suffers from the difficulty of calculating the thermodynamic properties of the transition state. 

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

Investigations to find such additive constituent properties of molecules go back to the 1920s and 1930s with work by Fajans [6] and others. In the 1940s and 1950s lhe focus had shifted to the estimation of thermodynamic properties of molecules such as heat of formation, AHf, entropy S°, and heat capacity, C°. 

The thermodynamic properties that we have considered so far, such as the internal energy, the pressure and the heat capacity are collectively known as the mechanical properties and can be routinely obtained from a Monte Carlo or molecular dynamics simulation. Other thermodynamic properties are difficult to determine accurately without resorting to special techniques. These are the so-called entropic or thermal properties the free energy, the chemical potential and the entropy itself. The difference between the mechanical emd thermal properties is that the mechanical properties are related to the derivative of the partition function whereas the thermal properties are directly related to the partition function itself. To illustrate the difference between these two classes of properties, let us consider the internal energy, U, and the Fielmholtz free energy, A. These are related to the partition function by ... 

Thermodynamic properties, such as enthalpy, energy, entropy, and the like, are related to one another. Thus, some information must be obtained from the... 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

Values for the free energy and enthalpy of formation, entropy, and ideal gas heat capacity of carbon monoxide as a function of temperature are listed in Table 2 (1). Thermodynamic properties have been reported from 70—300 K at pressures from 0.1—30 MPa (1—300 atm) (8,9) and from 0.1—120 MPa (1—1200 atm) (10). 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

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... 

Postiilate 5 affirms that the other molar or specific thermodynamic properties of PVT systems, such as internal energy U and entropy S, are also functions of temperature, pressure, and composition. Tnese molar or unit-mass properties, represented by the plain symbols U, and S, are independent of system size and are called intensive. Temperature, pressure, and the composition variables, such as mole fraction, are also intensive. Total-system properties (V U S ) do depend on system size, and are extensive. For a system containing n moles of fluid, M = nM, where M is a molar property. 

Enthalpy and Entropy as Eunctions of T and P At constant composition the molar thermodynamic properties are functions of temperature and pressure (Postulate 5). Tmns... 

The most satisfactory calciilational procedure for thermodynamic properties of gases and vapors requires PVT data and ideal gas heat capacities. The primary equations are based on the concept of the ideal gas state and the definitions of residual enthalpy anci residual entropy ... 

The thermodynamic properties of the solid silicates show the expected entropy change of formation from the constituent oxides of nearly zero, which is typical of the reaction type... 

The second method can be applied to mixtures as well as pure components. In this method the procedure is to find the final temperature by trial, assuming a final temperature and checking by entropy balance (correct when ASp t, = 0). As reduced conditions are required for reading the tables or charts of generalized thermodynamic properties, the pseudo critical temperature and pressure are used for the mixture. Entropy is computed by the relation. See reference 61 for details. ... 

The earliest hint that physics and information might be more than just casually related actually dates back at least as far as 1871 and the publication of James Clerk Maxwell s Theory of Heat, in which Maxwell introduced what has become known as the paradox of Maxwell s Demon. Maxwell postulated the existence of a hypothetical demon that positions himself by a hole separating two vessels, say A and B. While the vessels start out being at the same temperature, the demon selectively opens the hole only to either pass faster molecules from A to B or to pass slower molecules from B to A. Since this results in a systematic increase in B s temperature and a lowering of A s, it appears as though Maxwell s demon s actions violate the second law of thermodynamics the total entropy of any physical system can only increase, or, for totally reversible processes, remain the same it can never decrease. Maxwell was thus the first to recognize a connection between the thermodynamical properties of a gas (temperature, entropy, etc.) and the statistical properties of its constituent molecules. 

In principle, the second law can be used to determine whether a reaction is spontaneous. To do that, however, requires calculating the entropy change for the surroundings, which is not easy. We follow a conceptually simpler approach (Section 17.3), which deals only with the thermodynamic properties of chemical systems. 

There is thus assumed to be a one-to-one correspondence between the most probable distribution and the thermodynamic state. The equilibrium ensemble corresponding to any given thermodynamic state is then used to compute averages over the ensemble of other (not necessarily thermodynamic) properties of the systems represented in the ensemble. The first step in developing this theory is thus a suitable definition of the probability of a distribution in a collection of systems. In classical statistics we are familiar with the fact that the logarithm of the probability of a distribution w[n is — J(n) w n) In w n, and that the classical expression for entropy in the ensemble is20... 

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... 

Since we expect entropy to be extensive and behave like the other extensive thermodynamic properties, the integration constant must be equal to zero so that... 

As an example of the application of this procedure, Pitzer3 has calculated the thermodynamic properties for dimethylcadmium, including free rotation. At 298.15 K, he obtained the following result for the entropy ... 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

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