Heat Capacity and Free Energy

The crystal field interaction has pronounced effects on the heat capacity behavior of the system. At very low temperatures, ions occupy the lowest crystal field states. With increasing temperature, excitation within the crystal field spectrum takes place resulting in a significant contribution to the heat capacity (38). This contribution is given by the expression 

In the limit of low temperatures, it is easily seen that a plot of ln(CcpT2) vs T-1 gives a straight line, the slope of which is — E2/k. 

The free energy of the system at any temperature T under the influence of crystalline electric field may be calculated from the expression 

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The heat of formation (A//f) for 1,2,4-thiadiazole has been reported <90JPR885> but values for other thermodynamic functions (entropy, heat capacity, and free energy) are not available. 

Although the harmonic model does not provide a complete description for the motional properties of a protein because of the contribution of anharmonic terms to the potential energy, it is nevertheless of considerable importance because it does serve as a first approximation for which the theory is highly developed. Further, the harmonic model is essential for quantum mechanical treatments of vibrational contributions to the heat capacity and free energy [26, 27]. 

Melting and sublimation temperatures, internal energy (i.e., structural energy), enthalpy (i.e., heat content), heat capacity, entropy, free energy and chemical potential, thermodynamic activity, vapor pressure, solubility... 

In treating the various topics in this book the particular method employed has been determined in each case by considerations of simplicity, usefulness and logical development. In some instances the classical, historical approach has been preferred, but in others the discussion follows more modern lines. Whenever feasible the generalized procedures, involving reduced temperatures and pressures, which have been evolved in recent years chiefly by chemical engineers, are introduced. As regards statistical methods, the author feels that the time has come for them to take then-place as an essential part of chemical thermodynamics. Consequently, the applications of partition functions to the determination of heat capacities, entropies, free energies, equilibrium constants, etc., have been introduced into the text in the appropriate places where it is hoped their value will be appreciated. 

Busey and Giauque measured the heat capacity of nickel from 15 to 300 K. The entropy, heat content and free energy functions have been calculated. The authors used 99.98% nickel, in contrast to the numerous low temperature heat capacity studies quoted in this paper where rather low purity Ni-metal was investigated. Calculations of thermodynamic properties of nickel were extended to 800 K on the basis of available data. However, the results of such extrapolation seem to be less reliable. The standard molar entropy of Ni determined by Busey and Giauque was equal to 29.86 J-K -mol . ... 

In this chapter, the review will mainly focus on the laws of thermodynamics and their implications. The discussion includes concepts such as enthalpy, entropy, specific heat, heat capacity, Gibbs free energy, spontaneity of reactions, and related aspects. We have many ideas to discuss. So buckle up ... 

The final coefficient matrix, C, in Eqs. (9) and (10) can be used for further property prediction. It can regarded as the dynamical matrix in aimlysis of crystal vibrations by the Bom-Huang [11] formalism. Frequencies from the resulting vibrational dispersion curves can be used to compute the vibrational partition function. The latter leads to the vibrational free eneigy and heat capacity. The free energy may be useful in assessing relative stabilities of various crystal forms at finite temperatures. 

Sinke s tables of the thermodynamic properties of combustion products were prepared for the calculation of specific impulse and are not considered definitive or exhaustive. The tables list values of heat capacity, entropy, free energy function , enthalpy, enthalpy of formation, free energy of formation, and the logarithm of the equilibrium constant of formation from 298 to 6000 K at 100 K intervals. 

Haar et include values for the ideal thermodynamic functions, heat capacity, enthalpy, free energy, and entropy of a very wide range of hydrides, deuterides, and tritides. Much information is also given on exchange reactions. 

Physical Properties. Sulfur dioxide [7446-09-5] SO2, is a colorless gas with a characteristic pungent, choking odor. Its physical and thermodynamic properties ate Hsted in Table 8. Heat capacity, vapor pressure, heat of vaporization, density, surface tension, viscosity, thermal conductivity, heat of formation, and free energy of formation as functions of temperature ate available (213), as is a detailed discussion of the sulfur dioxide—water system (215). 

K, have been tabulated (2). Also given are data for superheated carbon dioxide vapor from 228 to 923 K at pressures from 7 to 7,000 kPa (1—1,000 psi). A graphical presentation of heat of formation, free energy of formation, heat of vaporization, surface tension, vapor pressure, Hquid and vapor heat capacities, densities, viscosities, and thermal conductivities has been provided (3). CompressibiHty factors of carbon dioxide from 268 to 473 K and 1,400—69,000 kPa (203—10,000 psi) are available (4). 

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

Thermod5mamics is a fundamental engineering science that has many applications to chemical reactor design. Here we give a summary of two important topics determination of heat capacities and heats of reaction for inclusion in energy balances, and determination of free energies of reaction to calculate equihbrium compositions and to aid in the determination of reverse reaction... 

Calorimetric measurements, when combined with the normally available room temperature thermodynamic properties, give values for free energy, enthalpy, heat capacity and even volume at high temperatures. 

Huffman, J.M., Parks, G.S., and Barmore, M. Thermal data on organic compounds. X. Further studies on the heat capacities, entropies and free energies of hydrocarbons, 7 Am. Chem. Soc., 53(10) 3876-3888,1931. 

Kelley, K.K. The heat capacity of toluene from 14K to 298K. The entropy and free energy of formation, J. Am. Chem. Soc., 51(9) 2738-2741,1929. 

Under the title Thermochemical Properties, both thermodynamic and thermal properties appear. These include thermodynamic properties, enthalpies of formation, Gibbs free energy of formation, entropies and heat capacities, and... 

All the above transitions are accompanied by changes in Seebeck coefficient, structural parameters, heat capacity and other characteristics. The V2O3 system has been explained in terms of a thermodynamic model which uses different free energy expressions for electrons in the itinerant and localized regimes (Honig Spalek, 1986). 

A major achievement of the free-electron model was to show why the contributions of the free electrons to the heat capacity and magnetic susceptibility of a metal are so small. According to Boltzmann statistics, the contribution to the former should be nkB per unit volume. According to Fermi-Dirac statistics, on the other hand, only a fraction of order kBT/ F of the electrons acquire any extra energy at temperature T, and these have extra energy of order kBT. Thus the specific heat is of order nfcBT/ F, and an evaluation of the constant gives... 

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