Blackbody Radiation

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

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

• Energy for a blackbody

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

• Entropy for a blackbody

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

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

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

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

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

• Energy for phonons

Applications

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