A New Mnemonic Scheme to Derive Thermodynamics Equations and Maxwell Relations Based on Butterfly Symmetry Approach

Yıl 2024, Sayı: Erken Görünüm - Early Pub Issues, 1 - 5

Reza Tariverdi Alireza Bahramian

Öz

In this study, a new mnemonic scheme is proposed for a simple closed system to derive equations in classical thermodynamics potentials that connect the state variables and Maxwell relations based on the butterfly symmetry approach. The proposed method does not have the difficulties in the arrangement and sign of parameters which were found in the geometric diagrams such as square, cub octahedron, concentric multi-circle, Venn diagram, and Natarajan’s thermodynamics circles. The suggested method resolves the identical elements and Maxwell's formulas in thermodynamics and energy, enthalpy, Helmholtz and Gibbs equations by creating a matrix through the butterfly symmetry strategy. The most important feature of this method is that the differential and partial derivatives of thermodynamic parameters are formed in matrix arrays. The signs are applied only according to the butterfly symmetry, and unlike the Max Born method, there is no need to pay attention to the direction of arrows.

Anahtar Kelimeler

Mnemonic scheme, Thermodynamics equations, Maxwell relations, Butterfly symmetry, simple novel method

Kaynakça

• J. F. Le Marechal and R. El Bilani, “Teaching and Learning Chemical Thermodynamics in School,” International Journal of Thermodynamics, vol. 11, no. 2, pp. 91-99, Jun. 2008, doi: 10.5541/ijot.216.
• M. V. Zemansky. Heat and Thermodynamics, New York: McGraw-Hill, 1968.
• L. Tisza. Generalized Thermodynamics, Cambridge: MIT Press, 1966.
• D. E. Christie. “Multipurpose mnemonic for thermodynamic equations,” American Journal of Physics, vol. 25, no. 1, pp. 486-487, Oct. 1957, doi: 10.1119/1.1934516.
• F. O. Koenig. “Families of thermodynamic equations. I The method of transformations by the characteristic group,” The Journal of Chemical Physics, vol. 3, no. 1, pp. 29-35, Jan. 1935, doi: 10.1063/1.1749549.
• H. B. Callen. Thermodynamics: An introduction to physical theories of equilibrium thermostatic and irreversible thermodynamics, New York: John Wiley & Sons Inc, 1960.
• S. F. Pate. “The thermodynamic cube: A mnemonic and learning device for students of classical thermodynamics,” American Journal of Physics, vol. 67, no. 1, pp. 1111-1113, Dec. 1999, doi: 10.1119/1.19093.
• J. E. Fieberg and Ch. A. Girard. “Mnemonic device for relating the eight thermodynamic state variables: The energy pie,” Journal of Chemical Education, vol. 88, no. 11, pp. 1544-1546, Aug. 2011, doi: 10.1021/ed100902z.
• J. C. Zhao. “A mnemonic scheme for thermodynamics,” MRS Bulletin, vol. 34, no. 2, pp. 92-94, Feb. 2009, doi: 10.1557/mrs2009.26.
• W. C. Kerr and J. C. Macosko. “Thermodynamic Venn diagrams: Sorting out forces, fluxes, and Legendre transforms,” American Journal of Physics, vol. 79, no. 9, pp. 950-953, Sep. 2011, doi: 10.1119/1.3599177.
• J. Venn. “On the diagrammatic and mechanical representation of propositions and reasoning,” Philosophical Magazine Series 5, vol. 58, no. 10, pp. 1-18, Jul. 1880, doi: 10.1080/14786448008626877.
• K. Natarajan. “Graphical summaries for Maxwell relations of closed and open thermodynamic systems,” International Journal of Mechanical Engineering Education, vol. 42, no. 1, pp. 1-17, Jul. 2014, doi: 10.7227/IJMEE.42.1.1.
• G. G. Bhagavanbhai, J. J. Bravo-Suarez and R. Kumar. “Fishing with scissors: A mnemonic for thermodynamic formula,” Oriental Journal of Chemistry, vol. 37, no. 3, pp. 700-703, May 2021, doi: 10.13005/ojc/370326.