C5300 Statistical Thermodynamics

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Mojmír Šob, DrSc. (lecturer)
prof. RNDr. Jan Vřešťál, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Vřešťál, DrSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Prerequisites
Basic knowledge of mathematics (university course) and physical chemistry (equilibrium, kinetics, chemical structure and quantum chemistry). M1010, M2010, C3140, C4020, C4060, C5020
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Course deals with following chapters: Molecular states and their distribution. Boltzmann distribution and partition function. Thermodynamic properties extracted from partition function. The internal energy and the entropy of perfect gas. Canonical ensemble and canonical partition function calculated for various modes of motion from spectroscopic data. Equilibrium constant. Statistical thermodynamics of real gases and fluids. Statistical thermodynamics of mixtures:regular solution model. Statistical thermodynamics of ideal crystal: Einstein and Debye models. Adsorption. Fluctuations. The aim of the course is to explain basic terms of statistical thermodynamics and outline possibilities of their application in chemistry.
Syllabus
  • 1.Statistical thermodynamics and molecular structure of matter. Postulates of statistical thermodynamics. Configuration and weight of state. Population of state. Most probable configuration. Lagrange multiplicators method, Boltzmann distribution. 2.Molecular partition function and its interpretation. Molecular partition function of harmonic oscillator. Calculation of population of states. Translation partition function. 3.Internal energy and entropy in statistical thermodynamics. Internal energy and partition function. Calculation of heat capacity at constant volume. Internal energy of perfect gas.Boltzmann formula for entropy. Calculation of entropy of oscillators ensamble. 4.Kanonical partition function. Mikrocanonical, canonical and grand-canonical ensamble. Partition function of canonical ensambles - most probable configuration. Calculation of internal energy and entropy by using of canonical partition function. Comparison of statistical and thermodynamic functions. Partition function of perfect gas. 5.Entropy of monoatomic gas. Sackur-Tetrode equation. Physical statistics. 6.Chemical applications of statistical thermodynamics. Calculation of Gibbs energy by use of partition function. Contributions to partition function: translational, vibrational, rotational and electronic. 7.Mean value of energy. Rotational and vibrational temperature. Ekvipartition principle. Calculation of heat capacity of gases. 8.Statistical description of chemical equilibrium. Calculation of equilibrium constant of chemical reaction by means of partition functions of reactants and products. 9.Statistical thermodynamics of real gas. Pair potentials. Configurational integral. Thermodynamic functions for pair interactions.Cluster formation. Virial coefficients. Residual entropy. 10.Statistical thermodynamics of liquids. Cell theory of liquids and compressed gases. Principle of corresponding states. Statistical expression of vapour-liquid equilibria. Theory of free volume of liquids. Calculation of pressure of saturated vapours. Distribution function in monoatomic liquids. Radial correlation function. 11.Statistical thermodynamics of crystal. Einstein and Debye models. Charakteristic temperatures. Fonons. 12.Vibrational and configurational entropy. Regular solution model. Model of polymer solution (Flory-Huggins). Adsorption. 13.Fluctuations of particles and thermodynamic properties. Statistics of fluctuations. Fluctuations of energy and of thermodynamic variables. Brownian motion. Relations between chemical equilibrium and chemical kinetics. Spontaneous organisation in systems.
Literature
  • BOUBLÍK, Tomáš. Statistická termodynamika. Vyd. 1. Praha: Academia, 1996, 199 s. ISBN 8020005668. info
  • ATKINS, P. W. Physical chemistry. 5th ed. Oxford: Oxford University Press, 1994, 1031 s. ISBN 0192690426. info
Teaching methods
Lectures focused to practical application in calculations of phase diagrams.
Assessment methods
Lectures organized weekly, oral exam at the end. Examples are as homeworks, check of results during lectures.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.