Thermo & Stat Mech - Spring 2006 Class 21 1 Thermodynamics and Statistical Mechanics Blackbody Radiation.

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Presentation transcript:

Thermo & Stat Mech - Spring 2006 Class 21 1 Thermodynamics and Statistical Mechanics Blackbody Radiation

Thermo & Stat Mech - Spring 2006 Class 212 Classical Energy Equipartition

Thermo & Stat Mech - Spring 2006 Class 213 Classical Energy Equipartition

Thermo & Stat Mech - Spring 2006 Class 214 Classical Energy Equipartition

Thermo & Stat Mech - Spring 2006 Class 215 Quantum Harmonic Oscillator

Thermo & Stat Mech - Spring 2006 Class 216 Energy of EM Waves in a Cavity Calculate the number of standing wave states in the frequency range between  and  + d . 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 217 Density of States (Lec 17)

Thermo & Stat Mech - Spring 2006 Class 218 Density of States for Photons

Thermo & Stat Mech - Spring 2006 Class 219 Photon Energy

Thermo & Stat Mech - Spring 2006 Class 2110 Photon Energy

Thermo & Stat Mech - Spring 2006 Class 2111 Graph

Thermo & Stat Mech - Spring 2006 Class 2112 Total Energy Density

Thermo & Stat Mech - Spring 2006 Class 2113 Energy Flux

Thermo & Stat Mech - Spring 2006 Class 2114 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 2115 Human Eye Peak at 555 nm

Thermo & Stat Mech - Spring 2006 Class 2116 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 2117 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 2118 Change to Wavelength

Thermo & Stat Mech - Spring 2006 Class 2119 Wavelength Spectrum

Thermo & Stat Mech - Spring 2006 Class 2120 Graph

Thermo & Stat Mech - Spring 2006 Class 2121 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 2122 Wien Displacement Law

Thermo & Stat Mech - Spring 2006 Class 2123 Photon Gas

Thermo & Stat Mech - Spring 2006 Class 2124 Helmholtz Function

Thermo & Stat Mech - Spring 2006 Class 2125 Pressure