The study of thermodynamics in the first and second years of university is a central subject in physical chemistry for chemistry majors. However, it introduces many new concepts that are not covered at all in middle and high school, making it a very difficult subject to understand. One particularly challenging concept is that while thermodynamic quantities as state functions are independent of the path, heat and work depend on the path. This can be compared to the elevation difference in mountain climbing, which is determined only by the difference in elevation between the starting point and the destination, whereas the cost and fatigue of climbing depend on the path taken (for example, whether one drives or walks). In this paper, we will examine representative reversible processes such as isothermal reversible processes, adiabatic reversible processes, isochoric reversible processes, and isobaric reversible processes. We will then consider the Carnot cycle, Stirling cycle, Otto cycle, and Diesel cycle, which are obtained through combinations of these representative reversible processes, and calculate heat, work, internal energy, enthalpy, entropy, Helmholtz energy, and Gibbs energy for each. While heat, work, internal energy, enthalpy, and entropy are described in textbooks used in universities,1, 2 the calculations for Helmholtz energy and Gibbs energy become very complex and are often not covered. However, we will discuss these in detail here. Recently, the concepts of thermodynamic functions such as enthalpy and entropy have started to appear in high school chemistry textbooks. However, high school students often have only a superficial understanding, knowing only the names of the functions. We hope that this paper can contribute even slightly to helping students understand thermodynamics more deeply when they advance to university without feeling bewildered. Note that in all derivations below, gases are assumed to be ideal gases.
Yamamoto et al. (Fri,) studied this question.