[01] Uchenna Okwudili Anekwe, Department of Physics, University of Science and Technology, Aleiro, Nigeria. [02] Emmanuel Hassan, Department of Physics, University of Science and Technology, Aleiro, Nigeria. [03] Oyidi Emmanuel Tunde, Department of Physics, University of Science and Technology, Aleiro, Nigeria.

P&V Independent involves the application of T&V independent together with the Application of second law of thermodynamics. The third TdS equation together with the first and second TdS equations has been known to many as the “tedious equations” due to a lot of derivations with resemblances involved. The TdS equations enables us to calculate the change of entropy during various reversible processes in terms of either dV and dT, or dP and dT, or dV and dP, and even in terms of directly measurable quantities such as the coefficient of expansion and the bulk modulus. This Manuscript involves another way of deriving the Thirds TdS equation applying the second law of thermodynamics together with equations already derived and introduced from the derivations of T&V which is also an application of the second law of thermodynamics.

Putting, Substituting, Eqn, Constant

[01] Expansion, Compression and The TdS equations, Chp 13 astrowww.phys.uvic.ca/~tatum/thermod/thermod13. [02] M. L. McGlashan, The use and misuse of the laws of thermodynamics”, J. Chem. Educ., May 1966, Vol. 43, No. 5, pp. 226-232. [03] C. P. Snow, “The two cultures and a second look”, Cambridge University Press, 1964, p. 15. [04] G. M. Barrow, “Thermodynamics should be built on energy – not on heat and work”, J. Chem. Educ., February 1988, Vol. 65, No. 2, pp. 122-125. [05] W. F. Harris, “The plethora of equilibrium constants”, Chem SA, November 1978, pp. 170-172. [06] G. Eriksson, “Thermodynamic studies of high temperature equilibria. III. SOLGAS, a computer program for calculating the composition and heat condition of an equilibrium mixture”, Acta Chem. Scand., Vol. 25, 1971, pp. 2651-2658. [07] G. Eriksson & E. Rosen, “Thermodynamic studies of high temperature equilibria. VIII. General equations for the calculation of equilibria in multiphase systems”, Chem. Scr., Vol. 4, 1973, pp. 193-194. [08] G. Eriksson, “Thermodynamic studies of high temperature equilibria. XII. SOLGASMIX, a computer program for calculation of equilibrium compositions in multiphase systems”, Chem. Scr., Vol. 8, 1975, pp. 100-103. [09] R. T. Jones, “Computer simulation of process routes for producing crude stainless steel”, MSc (Eng) Dissertation, University of the Witwatersrand, Johannesburg, 3 October 1989. [10] R. T. Jones & B. D. Botes, “Description of non-ideal slag and metal systems by the intermediate-compound method”, Proceedings of Colloquium on Ferrous Pyrometallurgy, SAIMM, Vanderbijlpark, 18 April 1989. [11] J. W. Hastie & D. W. Bonnell, “A predictive phase equilibrium model for multicomponent oxide mixtures: Part II. Oxides of Na-K-Ca-Mg-Al-Si”, High Temp. Sci., Vol. 19, 1985, pp. 275-306. [12] J. W. Hastie, W. S. Horton, E. R. Plante, & D. W. Bonnell, “Thermodynamic models of alkali-metal vapor transport in silicate systems”, High Temp. High Press., Vol. 14, 1982, pp. 669-679. [13] J. W. Hastie & D. W. Bonnell, “Thermodynamic activity predictions for molten slags and salts”, Abstract, Third International Conference on Molten Slags and Glasses, University of Strathclyde, Glasgow, 27-29 June 1988, The Institute of Metals. [14] H. Gaye, “A model for the representation of the thermodynamic properties of multicomponent slags”, University of Strathclyde, Metallurgy Department, Centenary Conference, June 1984, pp. 1-14. [15] Guggenheim, E. A. (1985). Thermodynamics. An Advanced Treatment for Chemists and Physicists, seventh edition, North Holland, Amsterdam, ISBN 0-444-86951-4. [16] Kittel, C. Kroemer, H. (1980). Thermal Physics, second edition, W. H. Freeman, San Francisco, ISBN 0-7167-1088-9. [17] Adkins, C. J. (1968). Equilibrium Thermodynamics, McGraw-Hill, London, ISBN 0-07-084057-1. [18] G., Jou, D., Casas-Vázquez, J. (2008). Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers, Springer, Berlin, ISBN 978-3-540-74252-4. [19] Chris Vuille; Serway, Raymond A.; Faughn, Jerry S. (2009). College physics. Belmont, CA: Brooks/Cole, Cengage Learning. p. 355. ISBN 0-495-38693-6. [20] H. Gaye & J. Welfringer, Proc. 2nd International Symposium on Metall. Slags and Fluxes, Ed. by H. A. Fine and D. R. Gaskell, Lake Tahoe, Nevada, AIME Publication, 1984, p. 357. [21] Hugh D. Young and Roger A. Freedman (2012) University Physics with Modern Physics. Pg 79 13th Ed. [22] Ike E. E (2014) Essential Principles of Physics, Jos ENIC publishers. [23] Katz, Debora M (2016) Physics for Scientists and Engineers: Foundations and Connections, Volume 1 Published by Cengage Learning. ISBN 13: 978053446675. [24] O. A. Oladipo (2017) PHY207 (Thermodynamics) - National Open University Available online at http: // www.nouedu.net [25] Lecture 3 (2017) First Law of Thermodynamics Available online at https://www2.ph.ed.ac.uk [26] Joseph M. Powers (2017) Lecture Notes on Thermodynamics.