Statistical Thermodynamics Lecture 1 Thermodynamics review Dr Ronald

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Statistical Thermodynamics Lecture 1: Thermodynamics review Dr. Ronald M. Levy ronlevy@temple. edu

Statistical Thermodynamics Lecture 1: Thermodynamics review Dr. Ronald M. Levy [email protected] edu

Chemical Physics: Statistical mechanics Chemical Physics: explain microscopic properties based on the properties of

Chemical Physics: Statistical mechanics Chemical Physics: explain microscopic properties based on the properties of individual molecules and molecular interactions Statistical Mechanics: Statisitical Mechanics Microscopic Atom Macroscopic Molecule Thermodynamics Themodynamics: Mathematical relation between experimental properties of macroscopic systems MQ. Chapter 1 volumetric thermal Isothermic compressibility expansion coefficient 1

The three laws of thermodynamics 2

The three laws of thermodynamics 2

Thermodynamic Potential: The differential form of first law of thermodynamics d. E = d.

Thermodynamic Potential: The differential form of first law of thermodynamics d. E = d. Q – d. W = Td. S – pd. V Independent Variable E (S, V) Thermodynamic Potential (S, V) Internal energy E (S, V) (T, V) Helmholtz free energy A (T, V) (T, p) Gibbs free energy G (T, p) (S, p) Enthalpy H (S, p) Done by Legendre transform 3

Legendre transformation Legendre Transforms: y(x) P 2 = dy/dx @(x 2, y 2) y(x)

Legendre transformation Legendre Transforms: y(x) P 2 = dy/dx @(x 2, y 2) y(x) P 1 = dy/dx @(x 1, y 1) Ψ(P) Ψ 1 Relation between the tangent and the intercept at any point on the function Ψ 2 (intercept) How do we find the inverse Legendre transforms? 4

Application of Legendre transform 5

Application of Legendre transform 5

Maxwell Relations and Thermodynamic square: V V T S S S P S Symmetric

Maxwell Relations and Thermodynamic square: V V T S S S P S Symmetric means + T Thermodynamic square F V T P E V P S P T G Asymmetric means - P 1 st Derivative Equation of state S P Gibbs free energy G V T H 2 st Derivative Maxwell relations 6