# Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - Department of Chemistry

Thermodynamics of Pure Compounds

## Thermodynamics of Pure Compounds

State, state functions and variables, partial derivatives as typical for measurement. Types of systems, examples. Internal energy and processes (1st Law): heat, (volume-)work, chemical work across appropriate walls change internal energy. Work on ideal gas under isothermal or adiabatic conditions. Internal energy of a pure compound: microscopic interpretation. Free energy. Enthalpy, its utility for processes at constant pressure. Heat capacities cp and cv; typical cp(T) of some compounds. Ideal gas, its equation of state, cv depending on microscopic degrees of freedom. Van-der-Waals gas. Heat of melting, vaporisation. Thermochemistry: Hess' law, heat of formation, reaction enthalpy. Standards, transfer terms from standard to actual state. Entropy and equilibrium (2nd law): from (differential) heat to differential entropy via integrating factor T, determination of s by integration of cp(T)/T. 2nd Law: properties of s(u) for a single system, maximisation of s=s1+s2 when systems are combined. Irreversibility. Entropy of melting, vaporisation. 3rd Law. — Mathematical intermezzo: f(x,y), partial derivatives, total differential df, Schwartz´ theorem, reconstruction of (relative) f by integrating partial derivatives. Slope of f along paths [for example f(x,y) =const giving (∂x/∂y)f, or path g(x,y)=const giving (∂f/∂x)g ]. Legendre-transformation of f(x,y), back transformation; examples. Thermodynamic relationships: thermodynamic potentials or Gibbs functions U, F, H, G as Legendre transforms when presented in terms of natural variables, state functions such as T(s,v,n) as first derivatives, material properties such as cP as second derivatives. Maxwell-Relations. Description of experiments generally by some (∂z/∂x)y., its systematic reduction to α, κ, Cp. Examples: internal pressure (∂U/∂V)S, (∂H/∂P)T, Joule-Thompson coefficient, (∂S/∂T)P = Cp/T, Cp-Cv.

General textbooks of Physical Chemistry:

G. Wedler, "Lehrbuch der Physikalischen Chemie", Wiley-VCH, 1997.
P. W. Atkins, "Physikalische Chemie", Wiley-VCH, 2002, "Physical Chemistry", Oxford University Press,
H. Kuhn und H.D. Försterling, "Principles of Physical Chemistry", Wiley 1999

Monographies on chemical thermodynamics

"Chemische Thermodynamik", Bd. 4 des Lehrwerks Chemie (Lehrbuch 4 und Arbeitsbuch 4), VEB Deutscher Verlag für Grundstoffindustrie, 1985.
U. Nickel, "Lehrbuch der Thermodynamik" (Neuerscheinung), 2. Aufl., PhysChem Verlag 2011,
ISBN 978-3-937744-06-3
H. + J. Rau, "Chemische Gleichgewichts-Thermodynamik", Springer Verlag, Heidelberg,
ISBN: 3 540 67065 3
Herbert B. Callen, Thermodynamics and an Introduction to Thermostatistics, Wiley 1985 ff.,
ISBN: 0 471 86256 8.
Arnold Sommerfeld, "Thermodynamik und Statistik", Harry Deutsch Verlag, Bd. 5, Vorlesungen über Theoretische Physik 1988,
ISBN: 3 87144-378.