1. Statistical Physics

2. Statistical Distribution Understanding the distribution of certain energy among particle members and their most probable behavior. E1 E2 E3 n(E) = g(E) f(E) n(E) : number of particles with energy E g(E) : number of state with energy E F(E) : distribution function average number of particles in each states with energy E probability of occupancy of each state with energy E

3. Statistical Distribution Law 1. Maxwell –Boltzmann Statistics Distribution of identical particles which are widely separated. Example: gas molecules 2. Bose Einstein Distribution For identical particles with spin 0 or integer/boson. Example: photon, phonon. 3. Fermi Diract Distribution For particles with odd half-integer spin/fermion (1/2, 3/2,...). Example: electron

5. Molecular Energy in Ideal Gas Following Maxwell-Botlzmann Distribution Imagine the particles are distributed within a sphere with radius p. Each particle in certain state with energy E has momentul p Number of momentum states Number of energy states

6. Number of molecules in energy state between E and dE To calculate C, use normalization for total molecules N Molecular Energy Distribution

7. Total energy of N molecule Average Molecular Energy

8. Distribution of Molecular Speed Average molecular speed The RMS speed

9. Planck Radiation Wien’s displacement Stefan-Boltzaman Law Energi radiated by an object per second

10. Specific Heat of Solids Classical internal Energy of solid Specific Heat at constant volume Dulong Petit law

11. Einstein Formula Average energy per oscilatorInternal Energy of Solid Einstein specific heat formula

12. Einstein Model at high temperature

13. Free electron contribution to specific heat