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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/statistical-thermodynamics
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课程名称：统计分子热力学 课程概述：本课程是物理化学的入门课程，探讨分子性质与宏观化学系统行为之间的联系。 课程大纲： - **模块1**：哲学观察热力学的重要性，介绍热力学实际应用的示例，帮助学生理解课程结束后能够预测的现象，如压力变化、温度变化和自发反应的方向。同时，概述原子和分子的量子化能级。 - **模块2**：首先接触气体的概念，尤其是状态方程，通过压力、体积、温度和粒子数之间的数学关系来描述气体行为。讨论理想气体、范德华气体和状态的维里方程，并研究真实气体的液-气图预测。 - **模块3**：深入研究集合和能级占有的统计概率，引入分配函数，描述如何从原子或分子分配函数组装集合分配函数，并推导集合的热力学性质。 - **模块4**：将特定分子性质与分子分配函数关联，推导原子、二原子和多原子理想气体的分配函数，并探讨量子化能级如何影响热力学性质。 - **模块5**：介绍热力学第一定律，讨论内能、热和功。强调内能作为状态函数和热、功作为路径函数，分析气体的PV功和热量传递的过程。 - **模块6**：引入熵这一新状态函数，探讨熵与无序程度的关系及其与热力学第二定律的关联，深入研究熵的统计基础并推导熵与分配函数的关系。 - **模块7**：轻量级模块，研究基于热力学第三定律的标准熵，比较从常压热容计算的第三定律熵与分子分配函数计算的熵。 - **模块8**：最后模块介绍亥姆霍兹和吉布斯自由能，推导这些状态函数在不同热力学集合中的作用，利用它们解释特定物质（如橡胶带）的行为。 - **期末考试**：这是课程的最终评分练习，包括20道题目，没有时间限制。 课程旨在帮助学生掌握分子热力学的基本理论与应用。
Name:Module 1
Description:This module includes philosophical observations on why it's valuable to have a broadly disseminated appreciation of thermodynamics, as well as some drive-by examples of thermodynamics in action, with the intent being to illustrate up front the practical utility of the science, and to provide students with an idea of precisely what they will indeed be able to do themselves upon completion of the course materials (e.g., predictions of pressure changes, temperature changes, and directions of spontaneous reactions). The other primary goal for this week is to summarize the quantized levels available to atoms and molecules in which energy can be stored. For those who have previously taken a course in elementary quantum mechanics, this will be a review. For others, there will be no requirement to follow precisely how the energy levels are derived--simply learning the final results that derive from quantum mechanics will inform our progress moving forward. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.
Name:Module 2
Description:This module begins our acquaintance with gases, and especially the concept of an "equation of state," which expresses a mathematical relationship between the pressure, volume, temperature, and number of particles for a given gas. We will consider the ideal, van der Waals, and virial equations of state, as well as others. The use of equations of state to predict liquid-vapor diagrams for real gases will be discussed, as will the commonality of real gas behaviors when subject to corresponding state conditions. We will finish by examining how interparticle interactions in real gases, which are by definition not present in ideal gases, lead to variations in gas properties and behavior. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.
Name:Module 3
Description:This module delves into the concepts of ensembles and the statistical probabilities associated with the occupation of energy levels. The partition function, which is to thermodynamics what the wave function is to quantum mechanics, is introduced and the manner in which the ensemble partition function can be assembled from atomic or molecular partition functions for ideal gases is described. The components that contribute to molecular ideal-gas partition functions are also described. Given specific partition functions, derivation of ensemble thermodynamic properties, like internal energy and constant volume heat capacity, are presented. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.
Name:Module 4
Description:This module connects specific molecular properties to associated molecular partition functions. In particular, we will derive partition functions for atomic, diatomic, and polyatomic ideal gases, exploring how their quantized energy levels, which depend on their masses, moments of inertia, vibrational frequencies, and electronic states, affect the partition function's value for given choices of temperature, volume, and number of gas particles. We will examine specific examples in order to see how individual molecular properties influence associated partition functions and, through that influence, thermodynamic properties. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.
Name:Module 5
Description:This module is the most extensive in the course, so you may want to set aside a little extra time this week to address all of the material. We will encounter the First Law of Thermodynamics and discuss the nature of internal energy, heat, and work. Especially, we will focus on internal energy as a state function and heat and work as path functions. We will examine how gases can do (or have done on them) pressure-volume (PV) work and how the nature of gas expansion (or compression) affects that work as well as possible heat transfer between the gas and its surroundings. We will examine the molecular level details of pressure that permit its derivation from the partition function. Finally, we will consider another state function, enthalpy, its associated constant pressure heat capacity, and their utilities in the context of making predictions of standard thermochemistries of reaction or phase change. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.
Name:Module 6
Description:This module introduces a new state function, entropy, that is in many respects more conceptually challenging than energy. The relationship of entropy to extent of disorder is established, and its governance by the Second Law of Thermodynamics is described. The role of entropy in dictating spontaneity in isolated systems is explored. The statistical underpinnings of entropy are established, including equations relating it to disorder, degeneracy, and probability. We derive the relationship between entropy and the partition function and establish the nature of the constant β in Boltzmann's famous equation for entropy. Finally, we consider the role of entropy in dictating the maximum efficiency that can be achieved by a heat engine based on consideration of the Carnot cycle. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.
Name:Module 7
Description:This module is relatively light, so if you've fallen a bit behind, you will possibly have the opportunity to catch up again. We examine the concept of the standard entropy made possible by the Third Law of Thermodynamics. The measurement of Third Law entropies from constant pressure heat capacities is explained and is compared for gases to values computed directly from molecular partition functions. The additivity of standard entropies is exploited to compute entropic changes for general chemical changes. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.
Name:Module 8
Description:This last module rounds out the course with the introduction of new state functions, namely, the Helmholtz and Gibbs free energies. The relevance of these state functions for predicting the direction of chemical processes in isothermal-isochoric and isothermal-isobaric ensembles, respectively, is derived. With the various state functions in hand, and with their respective definitions and knowledge of their so-called natural independent variables, Maxwell relations between different thermochemical properties are determined and employed to determine thermochemical quantities not readily subject to direct measurement (such as internal energy). Armed with a full thermochemical toolbox, we will explain the behavior of an elastomer (a rubber band, in this instance) as a function of temperature. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts. The final exam will offer you a chance to demonstrate your mastery of the entirety of the course material.
Name:Final Exam
Description:This is the final graded exercise (20 questions) for the course. There is no time limit to take the exam.
This introductory physical chemistry course examines the connections between molecular properties and the behavior of macroscopic chemical systems.
