Application of Higher Mathematics in Physics: “Taking the example of Thermodynamics”

CLC’s team led by Ms. Vasileia Chatzidogiannaki BSc. Physics (EKPA), MA Applied Mathematical and Physics Science (EMP), MA Physical and Technological Applications (EMP) and CLC’s Physics/Math teacher, and Ms. Panagiota Tsamtsakiri BSc. Math & MSc Statistics (Aristotle of Thessaloniki), Ph.D. candidate (AUEB) and CLC’s Math teacher, mentored and supervised our students Simos Michalopoulos, Philippos Kaloudis, and Philippos Tsoukis to carry out a research project on the Application of Higher Mathematics in Physics, based on the example of Thermodynamics.

There is a profound connection between mathematics and physics. This paper delves into the relationship between higher mathematics and the field of physics, with a specific focus on the application of advanced mathematical concepts within the realm of thermodynamics.  The paper commences with a series of examples of the pivotal role of higher mathematics in formulating and solving complex problems in physics. These examples span a wide range of topics, from calculus and linear algebra to group theory and complex analysis, showcasing how these mathematical techniques are instrumental in modeling and predicting the behavior of physical systems. Furthermore, this paper delves into the intricate alliance between advanced mathematics and the realms of thermodynamics and statistics, showcasing how mathematical rigor enriches our comprehension of complex physical systems. The paper continues with an exploration of the foundational principles of thermodynamics, elucidating concepts such as energy conservation, entropy, and the laws of thermodynamics.

Subsequently, it extends its reach to statistical mechanics, where probability theory and statistical methods provide essential tools for understanding and predicting random phenomena in the physical world. Through the example of the application of statistical thermodynamics on chemical reactions, the paper showcases how statistical thermodynamics can help us understand how the rate of a chemical reaction and the position of the equilibrium point between the forward and backward reactions is placed.

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