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Understanding Photon Statistics and Blackbody Radiation in Thermodynamics and Statistical Mechanics

Explore the calculation of photon states, Bose-Einstein statistics, and energy determination in various states. Analyze density of states, photon energy, and energy flux in a quantum harmonic oscillator system. Delve into the relationship between human eye sensitivity and solar energy. Investigate discrepancies in interpreting energy densities and wavelength peaks. Understand Wien's displacement law and the behavior of photon gas under different conditions.

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Understanding Photon Statistics and Blackbody Radiation in Thermodynamics and Statistical Mechanics

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  1. Photon Statistics and Blackbody Radiation Thermo & Stat Mech - Spring 2006 Class 21

  2. Classical Energy Equipartition Thermo & Stat Mech - Spring 2006 Class 21

  3. Classical Energy Equipartition Thermo & Stat Mech - Spring 2006 Class 21

  4. Classical Energy Equipartition Thermo & Stat Mech - Spring 2006 Class 21

  5. Quantum Harmonic Oscillator Thermo & Stat Mech - Spring 2006 Class 21

  6. Energy of EM Waves in a Cavity • Calculate the number of standing wave states in the frequency range between w and w + dw. Then Bose-Einstein statistics is used to determine the number of photons in each state. With that information the energy can be calculated. Thermo & Stat Mech - Spring 2006 Class 21

  7. Density of States (Lec 17) Thermo & Stat Mech - Spring 2006 Class 21

  8. Density of States for Photons Thermo & Stat Mech - Spring 2006 Class 21

  9. Photon Energy Thermo & Stat Mech - Spring 2006 Class 21

  10. Photon Energy Thermo & Stat Mech - Spring 2006 Class 21

  11. Graph Thermo & Stat Mech - Spring 2006 Class 21

  12. Total Energy Density Thermo & Stat Mech - Spring 2006 Class 21

  13. Energy Flux Thermo & Stat Mech - Spring 2006 Class 21

  14. Human Eye and the Sun • It is often stated in textbooks that the peak sensitivity of the human eye is at the wavelength at which the energy radiated by the sun is maximum. Thermo & Stat Mech - Spring 2006 Class 21

  15. Human Eye Peak at 555 nm Thermo & Stat Mech - Spring 2006 Class 21

  16. A Problem? • The graph of the energy density as a function of frequency, for a blackbody at a temperature of 5800 K, has a maximum at 1.41 eV. Photons of that energy have a wavelength of 879 nm, which is out of the visible spectrum, in the infrared. What is wrong? Thermo & Stat Mech - Spring 2006 Class 21

  17. Solution • The energy density is plotted as a function of energy, while the eye’s sensitivity is plotted as a function of wavelength. If we plot the energy density as a function of wavelength, its peak does not occur at 879 nm. How can this be? Thermo & Stat Mech - Spring 2006 Class 21

  18. Change to Wavelength Thermo & Stat Mech - Spring 2006 Class 21

  19. Wavelength Spectrum Thermo & Stat Mech - Spring 2006 Class 21

  20. Graph Thermo & Stat Mech - Spring 2006 Class 21

  21. Agreement • The maximum of the graph for 5800 K, the temperature of the sun’s surface has a maximum at 500 nm, in reasonable agreement with the peak sensitivity of the human eye. Thermo & Stat Mech - Spring 2006 Class 21

  22. Wien Displacement Law Thermo & Stat Mech - Spring 2006 Class 21

  23. Photon Gas Thermo & Stat Mech - Spring 2006 Class 21

  24. Helmholtz Function Thermo & Stat Mech - Spring 2006 Class 21

  25. Pressure Thermo & Stat Mech - Spring 2006 Class 21

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