Simplified thermochemical functions for tabulation
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IN the
last few y e a r s computer facilities have been used to tabulate thermodynamic functions of over 1000 inorganic substances at temperature intervals of 100 K, in the JANAF tables x for instance, which are being widely used. The new tables of Barin and Knacke are based on thermochemical data compiled e a r l i e r by Kubaschewski, Evans and Alcock ~ among others, and the results of more recently published investigations are now being updated. For many years the present authors have been involved in the use of thermodynamic functions in the calculation of chemical equilibria and energy balances for technical p r o c e s s e s . For this purpose the authors have found that the functions tabulated in the JANAF tables are not the simplest for application. F u r t h e r m o r e , some of the tabulated functions are not normally required whereas more desirable are m i s s ing. In this paper the authors deal with the question which functions should be chosen for tabulation. They have already been used in published tables s of data of' interest to metallurgists. Thermodynamic equilibrium is generally given by the principles of maximum entropy, minimum Gibbs energy or other equivalent conditions of this type. In t h e r m o c h e m i s t r y , the Gibbs energy G(T, P), which is uniquely determined by temperature T and p r e s s u r e P as independent variables, is widely used. This has to be a minimum in isobaric and isothermic variations, thus G T , p = m i n . a n d 6G T , p = O.
[1]
The Gibbs energy is related to the enthalpy H and the entropy S by definition, thus [2]
dG = d ( H - T S ) .
Isobaric variations are described by the differential equations, dSp = dHp/T,
[3a]
and I. BARIN is Wissenschaftlicher Assistant, and O. KNACKE is Professor, Lehrstuhl ftir Metallurgie der Kernbrennstoffe und Theoretische HSttenkund, Technische Hochschule Aachen, Germany. Manuscript submitted August 15, 1972. METALLURGICAL TRANSACTIONS
dGp = - SpdT, [3b] where the suffix P denotes constant p r e s s u r e . The integration of these Eqs. leads to, T drip
S=S(To) + f T To and
[4] T
G = H(To) - T . S ( T o) -
T drip
f
f dT T [5] To To in which S(To) and H (To) are considered to be integration constants. It is generally agreed to choose for the entropy integration constants according to the third law of t h e r modynamics, and the resultant values are tabulated. For the enthalpy a definition different from that of JANAF will be introduced below. In a system in which no material exchange with the surroundings takes place, the integration constants may be chosen arbitrarily. However in open chemical systems the integration constants must be chosen to give c o r r e c t results for a) the equilibrium constants, b) the energy balance of any chemical p r o c e s s that is not usually isothermic in practice e.g., the shaft furnace and the converter, and c) the properties of homogenous mixtures or solutions. If these conditions are fulfilled at any temperature, e . g . , the reference temperature To, they hold for all other tem
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