Blackbody Radiation

#Physics
When light is emitted from a hot body due to the thermal excitations wiggling charges in the object

Topics

• Stefan-Boltzmann Law
• Debye Temperature
• Ultraviolet Catastrophe

$\displaystyle U=\frac{\pi ^{2}}{15(\hbar c)^{3}}V\tau ^{3}$

• Energy for a blackbody

$\displaystyle \sigma=\frac{4\pi ^{2}V\tau ^{3}}{45(\hbar c)^{3}}$

• Entropy for a blackbody

$\displaystyle N_{\gamma}=\frac{2}{\pi ^{2}}\left( \frac{\tau}{\hbar c} \right)^{3}V\zeta(3)\approx \frac{\sigma}{3.6}$

• Number of photons in a certain volume
• $\displaystyle \zeta$ is the Riemann Zeta function

$\displaystyle n_{D}=\left( \frac{6N}{\pi} \right)^{1/3}$

• Debye number
• Gives the max $\displaystyle k$ for $\displaystyle N$ particles

$\displaystyle U=3N\tau=\hbar v_{\text{sound}}\left( \frac{\pi}{L} \right)n$

• Energy for phonons

Applications

• Toaster
• Sun
• IR Thermometry
• Imaging
• CMB ($\displaystyle 2.7\mathrm{\text{ }K}^\circ$)
• Blackholes/Hawking Radiation
• Unruh Radiation
• Voltage/coment noise across resistor Johnson-Nyquist noise (1D bbody radiation)