Proposal for determining changes in entropy of semi ideal gas using mean values of temperature functions

• Published in: Hemijska industrija 2014-01, Vol.68 (5), p.615-628
• Main Authors: Pejovic, Branko, Micic, Vladan, Perusic, Mitar, Tadic, Goran, Vasiljevic, Ljubica, Smiljanic, Slavko
• Format: Article
• Language: English
• Subjects: approximate functions; Calculus; differential and integral calculus; Differential calculus; Enthalpy; Entropy; Functions (mathematics); Gases; graphical methods; Graphical representations; Heat; Heat exchange; Ideal gas; Integrals; Internal energy; Mathematical analysis; Mathematical models; mean and true specific heat capacity; semi-ideal gas; Specific heat; table value functions; the change in entropy; the mean value of the function; Transformations (mathematics)
• ISSN: 0367-598X; 2217-7426
• DOI: 10.2298/HEMIND130825090P

In a semi-ideal gas, entropy changes cannot be determined through the medium specific heat capacity in a manner as determined by the change of internal energy and enthalpy, i.e. the amount of heat exchanged. Taking this into account, the authors conducted two models through which it is possible to determine the change in the specific entropy of a semi-ideal gas for arbitrary temperature interval using the spread sheet method, using the mean values of the appropriate functions. The idea is to replace integration, which occurs here in evitably, with mean values of the previous functions. The models are derived based on the functional dependence of the actual specific heat capacity on the temperature. The theorem used is that of the mean value of a function as well as the mathematical properties of the definite integral. The mean value of a fractional function is determined via its integrand while the logarithmic functions were performed by applying a suitable transformation of the differential calculus. The relations derived relation, using the computer program, have enabled the design of appropriate thermodynamic tables through which it is possible to determine the change in entropy of arbitrary state changes in an efficient and rational manner, without the use of calculus or finished forms. In this way, the change in the entropy of a semi-ideal gas is determined for an arbitrary temperature interval using the method which is analogous to that applied in determining the change of internal energy and enthalpy or the amount of heat exchanged, which was the goal of the work. Verification of the proposed method for both the above functions was performed for a a few characteristic semi-ideal gases where change c(T) is significant, for the three adopted temperature intervals, for the characteristic change of state. This was compared to the results of the classical integral and the proposed method through the prepared tables. In certain or special cases, it is possible to apply the presented method also in determining the change in entropy of the real gas. Apart from that, the paper shows that the change in entropy for the observed characteristic case can be represented or graphically determined using the planimetric method of diagrams with suitably selected coordinates. nema