大学初年級における自由エネルギー概念の学習法
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Whereas the First Law of Thermodynamics seems easy to understand, since the idea of conservation of energy is familiar in elementary learning, this is not the case with the Second Law. During their earlier years at college most of the students find difficulty in learning the meaning and content of the Second Law and in appreciating its usefulness for other branches of natural sciences. The idea of the Second Law of Thermodynamics is closely related to a general principle of dissipation of energy, stating that all irreversible changes tend to produce unavailable energy and degrade the capacity for doing work. Although students have trouble in understanding the concept of entropy, which is introduced to express quantitatively the dissipation of energy, they find even more difficulty in catching the meanings of Helmholtz and Gibbs free energies. These two free energy are known as the thermodynamic potentials which serve as indicators for the irreversible change, depending on the various experimental conditions under which the physico-chemical changes take place. Students are therefore discouraged in working out the concept of free energies which are very important for chemistry. General speaking, most theories of thermodynamics are developed from abstract concepts to practical problems. In textbooks the definitions of free energies are described in relationship to other thermodynamic functions, thus giving the students the impression that the definition are abstract. But the students would not have difficulties, if they properly understood the mean ings of definitions and their theoretical development to practical problems. However, the concept of free energies does not seem easy to understand correctly so that it is likely to cause misunder-standing. Thus in many cases students can not improve in their effort to learn, for they proceed in their learning without a full understanding of free energy. Even though theories in the natural sciences are developed from abstract concepts, it is very important to appreciate the relationships between theory and reality, for natural science is human thinking based on a sensual recognition of the nature. The author proposes a new way of learning free energy, in order to incorporate the concepts mentioned above. The author's proposal for learning free energy is to reverse the traditional learning procedure taken in the textbooks published up to the present time. The students should learn the meaning of free energy first and then the students should drive for themselves the formula for free energy funcitions, A=E-TS (1)G=H-TS (2) where A and G are Helmholtz and Gibbs Free Energies respectively. The author believes that his proposal for the learning procedure suits the historical development of free energy concepts which are described in this article. In order to explain free energy, several practical examples are given, including free exansion of a gas, work done by osmotic pressure and electrical work done by a chemical reaction. From these the important relationship: G=A+PV (3) is derived. It is also explained in detail that the relationship between G and A holds even in the pure state of the ideal gas. The contents of this article are as following; I. A reason why a new method of learning should be proposed. II. The historical development of the concept of free energy. III. A new proposal for learning free energy. New Way for Learning the Concept of Free Energy in the Earlier Yearsat 179 IV. 1 Traditional procedure of learning. 2 A new way proposed for learning. 2. 1 Free expansion of gas. 2.2 Holmholtz free energy or work function. 2.3 Gibbs free energy or available energy. a. Work done by osmotic pressure. b. Electrical work done by a chemical reaction. 2.4 Free energy of gas. 2.5 Thermodynamic functions and conditions of equilibrium. V. Summary In physical chemistry, Helmholtz and Gibbs free energies play very important roles as indicators for physico-chemical equilibriums. According to the traditional descriptions of equilibrium are derived from the free energy functions given by Gibbs. However, the same conclusions are obtained directly from Clausius's original idea for the free energy which is described by the relationship; W_T=A or δW_T=dA (4) where W is the maximum work done by a reversible change in the system at constent temperature and A is the free energy change of the system. If the only external work is due to a volume change, W_T=-Pd V, therefore (PdV+dA)_T=0 (5) This gives the condition for equilibrium at constant temperature and volume (PdV=0), since reversible change is possible only if the system is in equilibrium (dA)_<T.V>=0 For an infinitesmal change, (3) gives dG=dA+PdV+VdP (7) But if T is constant, (dG)_T=(dA+PdV)_T+(VdP)_T (8) and (5) gives for equilibrium (dG-VdP)_T=0 (9) and hence if P is also constant (dP=0) (dG)_<T.P>=0 (10) and again it is inferred that (9) is the condition of equilibrium at constant temperature and pressure. Thus it is advisable to understand the physical meaning of equations (3) and (4) first it elementary learning, because the equilibrium conditions are derived directly from these equations.
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