Newton’s Method Cubic Equation of State C++ Source Code for Iterative Volume Computation

  IJETT-book-cover  International Journal of Recent Engineering Science (IJRES)          
  
© 2021 by IJRES Journal
Volume-8 Issue-3
Year of Publication : 2021
Authors : Abdulhalim Musa Abubakar, Ahmad Abubakar Mustapha
  10.14445/23497157/IJRES-V8I3P103

MLA 

MLA Style: Abdulhalim Musa Abubakar, Ahmad Abubakar Mustapha  "Newton’s Method Cubic Equation of State C++ Source Code for Iterative Volume Computation"International Journal of Recent Engineering Science 8.3(2021):12-22. 

APA Style: Abdulhalim Musa Abubakar, Ahmad Abubakar Mustapha. Newton’s Method Cubic Equation of State C++ Source Code for Iterative Volume Computation  International Journal of Recent Engineering Science, 8(3), 12-22.

Abstract
This write-up enumerates the basic cubic equations of state used for pressure, volume and temperature determination for pure substances. It however focuses on developing a Dev C++ program for molar volume computation. Since molar volume in all cubic equations of state appears unsolvable due to their non-linear nature, numerical solution methods, one of which is Newton-Raphson method can be utilize to estimate the root of such polynomial equations. The 257 line of code running from Figure 1 to Figure 6, if executed, will return the molar volume to some certain iteration over a tolerance error specified. The program is a 4-in-1 calculator. The user is capable of working with a desired equation of state at a time. User should note that the source code converges for either large or small error specified.

Reference
[1] Deiters, Ulrich K and Ricardo Macías-Salinas. Calculation of Densities from Cubic Equations of State: Revisited. Industrial & Engineering Chemistry Research (2014): 2529−2536. <pubs.acs.org/IECR>.
[2] Ghosh, Pallab. Numerical Methods with Computer Programs in C++. Delhi: PHI Learning Private Limited, 2009. <http://www.kopykitab.com/product/7407>.
[3] Himmelblau, David M and James B Riggs. Basic Principles and Calculations in Chemical Engineering. 5th. New Jersey: Prentice Hall, 1982.
[4] Housam, Binous and Nasri Zakia. Applications of the Soave–Redlich–Kwong Equation of State Using Mathematica. Journal of Chemical Engineering of Japan 10.6 (2007): 534–538. <https://www.researchgate.net/publication/239269619>.
[5] Housam, Binous and Zakia Nasri. Applications of the peng-robinson equation of state using MATLAB. Chemical Engineering Education (2015): 1-11. <https://www.researchgate.net/publication/279621077>.
[6] Mansour, Eman Mohamed. Equation of State. Cairo: IntechOpen, 2020.
[7] Mate, Attila. Introduction to Numerical Analysis with C Program. New York: Brooklyn College of the City University of New York, 2014.
[8] Oliveira, M B, et al. Modeling Phase Equilibria Relevant to Biodiesel Production: A Comparison of gE Models, Cubic EoS, EoS-gE and Association EoS,. Industrial & Engineering Chemistry and Research 50 (2011): 2348–2358.
[9] Sahay, Ramdharee, Muzenda Edison and Belaid Mohamed. A Review of the Equations of State and their Applicability in Phase Equilibrium Modeling. International Conference on Chemical and Environmental Engineering (ICCEE'2013) . Johannesburg, 2013. 1-4.
[10] Soedarto, S H. Ratnawati. Improvement of the Redlich-Kwong Equation of State By Modification of Co-Volume Parameter. Vol. 13. Semarang, 2010. 8-65.

Keywords
C++ Program, Cubic Equations of State, Equation of state, Newton’s Method, Iteration