Heat Q vs Work W and efficiency Carnot cycle reversible Maximal efficiency depends on (TH -TC) Transformation of heat into work always involves losses (QC) 1824 Sadi Carnot (1796-1832)

Fundaments of thermodynamics First law: conservation of energy U Rudolf Clausius 1822-1888 Second law: transformations (processes) 1854 Äquivalenzwert der Verwandlung R. Clausius Philosophical Magazine, 12 (1856) p.81

Statistical thermodynamics: History Daniel Bernouilli 1700-1782 Hydrodynamica (1738): Heat = kinetic (movement) energy

Statistical thermodynamics: History James Maxwell 1831-1879 1859: Maxwell distribution of velocities in gases

Statistical thermodynamics: History Maxwell-Boltzmann distribution Boltzmann Transport Equation (BTE) Number of molecules with velocity v Ludwig Boltzmann 1844-1906 1896: Lectures on gas theory

Statistical thermodynamic Entropy 1877: Boltzmann entropy S measure for “statistical mixedupness” Ω number of micro states of a system in equilibrium as a macro state Ludwig Boltzmann 1844-1906

Statistical thermodynamic Entropy Ω number of micro states of a system in equilibrium as a macro state Ludwig Boltzmann 1844-1906

Statistical thermodynamic Entropy Ω number of micro states of a system in equilibrium as a macro state Max Planck 1858-1947 Boltzmann constant

Statistical thermodynamic Entropy S increases with temperature Ludwig Boltzmann 1844-1906

Statistical thermodynamic Entropy Ludwig Boltzmann 1844-1906

Modern classical thermodynamics Third law (Nernst) Hermann Walther Nernst 1864-1941

Statistical thermodynamics: History Boltzmann distribution Average number of molecules with energy εi Erwin Schrödinger 1887-1964 Quantum mechanics: discrete energy states εi

Statistical thermodynamics: History Boltzmann distribution Chance of molecule to have energy εi Entropy of the system Erwin Schrödinger 1887-1964

Statistical thermodynamics: History Boltzmann Transport Equation (BTE) Ludwig Boltzmann 1844-1906 1896: Lectures on gas theory

Statistical thermodynamic Entropy Zentralfriedhof Vienna Ludwig Boltzmann 1844-1906

Statistical Thermodynamics : Boltzmann distribution Two level system

Statistical Thermodynamics: Boltzmann distribution