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Received August 31, 2022
Accepted November 8, 2022
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엔트로피와 분자 특성, 상 및 성분의 관계
Entropy and its Relation with the Property of Molecule, Phase and Component
서울시립대학교 화학공학과, 02504 서울시 동대문구 서울시립대길 163
Department of Chemical Engineering, University of Seoul, 163 Seoulsiripdaero, Dongdaemun-gu, Seoul, 02504, Korea
changjaee@uos.ac.kr
Korean Chemical Engineering Research, February 2023, 61(1), 116-122(7), 10.9713/kcer.2023.61.1.116 Epub 26 January 2023
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Abstract
열역학 계를 구성하는 분자들의 특성, 거시적 규정의 성분, 상의 종류가 엔트로피에 미치는 관련성을 고찰하였다. 같은 성분에 속하는 분자들의 불구별성에 대하여 고전역학과 양자역학의 관점의 차이를 이해하고, 분자의 특성이 거시적 분 류의 기준인 ‘성분’과 부합하는가를 검토하였다. 계의 열역학적 미시 상태에 관한 정의를 명확히 함으로써 분자의 구 별성에 기인하는 볼츠만 통계학의 결함을 제거하고, 그 결과로 엔트로피에 대한 깁스 역설이 해소된다. 유체 및 고체의 상 변화에서 분자의 불구별성, 대칭수, 그리고 실현되는 미시 상태들의 수의 변화가 분배 함수와 엔트로피에 미치는 영향을 고찰하였다. 특히, 결정성 고체는 에르고딕 가설을 따르지 않는 열역학 계로 다룰 수 있음을 보인다.
We study the relationship of entropy with the properties of molecules and also with the macroscopic specifications of the system, i.e., component and phase. Understanding different viewpoints of classical mechanics and quantum mechanics for the indistinguishability of molecules belonging to the same component, we discuss a few thermodynamic systems in which the properties of molecules are to be consistent with the component as a macroscopic term of classifying the molecules. With a clear definition of thermodynamic microstate, the drawback of the Boltzmann statistics caused by the distinguishability of molecules is avoided, and the Gibbs paradox of entropy consequently disappears. Corresponding to the characteristics of fluid and solid phases, we investigated the effects of the indistinguishability and the symmetry number of molecules and the number of microstates realized in time on the partition function and the entropy. In particular, we show that crystalline solid can be regarded as a system which does not satisfy the ergodic hypothesis.
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Flory PJ, Principles of Polymer Chemistry, Cornell University Press(1953).
Nagle JF, J. Stat. Phys., 117, 1047 (2004)
Gray CG, Gubbins KE, Theory of Molecular Fluids - Vol 1: Fundamentals, Oxford University Press, New York (1984).
Frenkel D, Smit B, Understanding Molecular Simulation 2nd ed., Academic Press (2002).
Sprik M, Cheng A, Klein ML, J. Phys. Chem., 96, 2027 (1992)
Chang J, Sandler SI, J. Chem. Phys., 125, 054705 (2006)
Kim M, Chang J, Sandler SI, J. Chem. Phys., 140, 084110 (2014)
