Statistical Molecular Thermodynamics from Coursera

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Syllabus

Module 1

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.

Module 2

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.

Module 3

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.

Module 4

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.

Module 5

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.

Module 6

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.

Module 7

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.

Module 8

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.

Final Exam

This is the final graded exercise (20 questions) for the course. There is no time limit to take the exam.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Delves into molecular level details of pressure, permitting its derivation from the partition function

Uses statistical mechanics to derive macroscopic properties from molecular properties

Covers principles underlying both classical and quantum systems

Provides a comprehensive overview of physical chemistry principles

Suitable for students with a background in physics, chemistry, or engineering

Emphasizes the connections between microscopic and macroscopic properties of matter

Reviews summary

Highly-rated molecular thermodynamics course

Learners overwhelmingly say this course is excellent. They describe it as engaging and well-structured. The demonstrations and experiments are especially helpful for understanding the concepts.

Course is challenging but rewarding

"The most awesome Coursera course I took so far."

"This was one of the best courses that I've taken online."

"The assignments,on-spot assessment questions between video clips are of very good standard and also well documented and well explained."

Concepts are well-explained and easy to understand

"Theoretically sound concepts were well linked to relevant practicability."

"The course content was very good and easy to understand as well."

"The demonstrations were awesome"

Instructor is knowledgeable and engaging

"Dr. Cramer does an excellent job of connecting the abstract concepts with concrete examples to help you really understand/appreciate the underlying relationships."

"Excellent content, and a very competent instructor who knows his stuff."

"Professor have first mentioned in lectures about patent office in USA, then we have studied, in final exam, Professor says about patent office judgements."

May require prior knowledge of thermodynamics

"Though this course is categorized as beginner level,having some prior knowledge of thermodynamics will be helpful."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Statistical Molecular Thermodynamics with these activities:

Read Atkins' Inorganic Chemistry

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Atkins' Inorganic Chemistry is a classic textbook that provides a comprehensive overview of inorganic chemistry. This book will help you to understand the basic principles of thermodynamics and how they apply to inorganic systems.

View Physical Chemistry for the Life Sciences on Amazon

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Read through the chapters on thermodynamics.
Take notes on the key concepts.
Do the practice problems at the end of each chapter.

Review Chemical Equations

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Reviewing chemical equations and stoichiometry will help you understand the language of chemistry and how to interpret and manipulate chemical reactions. This will give you a strong foundation for the rest of the course.

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Read through your notes or textbook on chemical equations and stoichiometry.
Practice balancing chemical equations.
Do some practice problems on stoichiometry.

Organize Your Notes

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Organizing your notes will help you to stay on top of the material and to be better prepared for exams.

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Go through your notes and make sure that they are complete.
Organize your notes into a logical order.
Create a system for storing and retrieving your notes.

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Join a Study Group

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Joining a study group will allow you to discuss the course material with other students and get help with difficult concepts. This can be a great way to improve your understanding of the material and to prepare for exams.

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Find a study group that meets regularly.
Attend the study group meetings and participate in the discussions.
Help other students with their questions.

Solve Thermodynamics Problems

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Solving practice problems will help you develop your problem-solving skills and apply the concepts of thermodynamics to real-world situations.

Browse courses on Thermodynamics

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Find a set of practice problems on thermodynamics.
Solve the problems.
Check your answers against the answer key.

Learn about Molecular Partition Functions

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Molecular partition functions are a key concept in thermodynamics and statistical mechanics. By understanding how to calculate and interpret partition functions, you will gain a deeper understanding of the behavior of molecules and their interactions.

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Find a tutorial on molecular partition functions.
Watch the tutorial and take notes.
Try to apply the concepts you learned to some practice problems.

Build a Thermodynamics Calculator

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Building a thermodynamics calculator will help you to apply your knowledge of thermodynamics to a practical problem. This will help you to see how thermodynamics can be used to solve real-world problems.

Browse courses on Thermodynamics

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Choose a programming language and development environment.
Design the interface of your calculator.
Write the code for your calculator.
Test your calculator against known results.

Develop a Thermodynamics Model

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Developing a thermodynamics model will allow you to apply the concepts of thermodynamics to a real-world problem. This will help you to see how thermodynamics can be used to solve practical problems.

Browse courses on Thermodynamics

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Identify a problem that can be solved using thermodynamics.
Develop a mathematical model of the problem.
Use the model to make predictions about the behavior of the system.
Test the model against experimental data.

Career center

Learners who complete Statistical Molecular Thermodynamics will develop knowledge and skills that may be useful to these careers:

Physical Chemist

Physical chemists study the physical properties of matter. This work can help us to understand the behavior of matter and to develop new materials and technologies. Statistical Molecular Thermodynamics is a fundamental tool for physical chemists.

See salaries and explore the career path for Physical Chemist

Theoretical Chemist

Theoretical chemists use mathematical models to study the behavior of atoms and molecules. This work can help us to understand the fundamental principles of chemistry and to develop new theories. Statistical Molecular Thermodynamics is a key area of research for theoretical chemists.

See salaries and explore the career path for Theoretical Chemist

Computational Chemist

Computational chemists use computers to study the behavior of atoms and molecules. This work can help us to understand the fundamental principles of chemistry and to develop new theories. Statistical Molecular Thermodynamics is a key area of research for computational chemists.

See salaries and explore the career path for Computational Chemist

Quantum Chemist

Quantum chemists use quantum mechanics to study the behavior of atoms and molecules. This work can help us to understand the fundamental principles of chemistry and to develop new theories. Statistical Molecular Thermodynamics is a key area of research for quantum chemists.

See salaries and explore the career path for Quantum Chemist

Chemical Engineer

Chemical engineers use their understanding of chemistry to design and operate chemical processes. This work helps to produce a wide variety of products, from gasoline to pharmaceuticals. Statistical Molecular Thermodynamics can help chemical engineers to develop new processes that are more efficient and environmentally friendly.

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Materials Scientist

Materials scientists develop new materials with improved properties. This work can lead to the development of new products, such as stronger and lighter materials for use in cars and airplanes. Statistical Molecular Thermodynamics can help materials scientists to understand the properties of materials and to design new materials with specific properties.

See salaries and explore the career path for Materials Scientist

Polymer Scientist

Polymer scientists develop new polymers, which are used in a wide variety of products, from plastics to rubber. Statistical Molecular Thermodynamics can help polymer scientists to understand the properties of polymers and to design new polymers with specific properties.

See salaries and explore the career path for Polymer Scientist

Nanotechnologist

Nanotechnologists use nanotechnology to develop new materials and devices. This work can help us to solve some of the world's most challenging problems, such as energy and climate change. Statistical Molecular Thermodynamics can help nanotechnologists to understand the properties of nanomaterials and to design new nanomaterials with specific properties.

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Biochemist

Biochemists study the chemical processes that occur in living organisms. This work can help us to understand how living organisms function and to develop new treatments for diseases. Statistical Molecular Thermodynamics can help biochemists to understand the interactions between molecules in living organisms.

See salaries and explore the career path for Biochemist

Pharmaceutical Scientist

Pharmaceutical scientists develop new drugs and treatments for diseases. This work can help to improve the lives of people around the world. Statistical Molecular Thermodynamics can help pharmaceutical scientists to understand the interactions between drugs and the human body.

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Environmental Scientist

Environmental scientists study the environment and the impact of human activities on the environment. This work can help us to protect the environment and to develop sustainable ways to use resources. Statistical Molecular Thermodynamics can help environmental scientists to understand the chemical processes that occur in the environment.

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Technical Writer

Technical writers create technical documentation, such as user manuals and technical reports. This work can help to communicate complex technical information to a variety of audiences. Statistical Molecular Thermodynamics may be useful for technical writers who need to write about physical chemistry.

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Teacher

Teachers educate students at all levels, from elementary school to university. This work can help to inspire students to learn about science and to pursue careers in science. Statistical Molecular Thermodynamics may be useful for teachers who want to teach physical chemistry.

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Patent Attorney

Patent attorneys help inventors to obtain patents for their inventions. This work can help to protect the rights of inventors and to promote innovation. Statistical Molecular Thermodynamics may be useful for patent attorneys who specialize in patents related to physical chemistry.

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Science Writer

Science writers communicate complex scientific information to the public. This work can help to educate the public about science and to promote scientific literacy. Statistical Molecular Thermodynamics may be useful for science writers who want to write about the latest advances in physical chemistry.

See salaries and explore the career path for Science Writer

Reading list

We've selected seven books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Statistical Molecular Thermodynamics.

Molecular Theory of Capillarity

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Provides a comprehensive overview of statistical thermodynamics, including its fundamental concepts and applications. It valuable resource for students and researchers in the field.

Molecular Theory of Capillarity

Paperback

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Molecular Theory of Capillarity

Kindle Edition

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Thermodynamics and Statistical Mechanics

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Provides a comprehensive and rigorous treatment of thermodynamics and statistical mechanics. It valuable resource for students and researchers in the field.

Thermodynamics and Statistical Mechanics (Classical...

Kindle Edition

$$$

Commonly Asked Questions in Thermodynamics

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Provides a comprehensive treatment of the molecular thermodynamics of fluid-phase equilibria. It valuable resource for students and researchers in the field.

Commonly Asked Questions in Thermodynamics

Kindle Edition

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Statistical Mechanics: Theory and Molecular...

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Provides a comprehensive and modern treatment of statistical mechanics. It valuable resource for students and researchers in the field.

Statistical Mechanics: Theory and Molecular...

Hardcover

$$$

Statistical Mechanics: Theory and Molecular...

Kindle Edition

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Mathematical Foundations of Thermodynamics

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Provides a comprehensive and rigorous treatment of the fundamentals of statistical thermodynamics. It valuable resource for students and researchers in the field.

Mathematical Foundations of Thermodynamics:...

Kindle Edition

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