PX158 - F1 - black body radiation

planck's law

• all bodies emit thermal radiation
• a black body absorbs perfectly at all wavelengths
• for a black body, the wavelength, $\lambda$, of the emitted radiation can be specified
• in 1901, max planck found a function and model that accurately gave the spectrum of black body.
• power per area per $\lambda :$

• "rayleigh-jeans tail" can be obtained from classical physics
• smooth curves
• steep cut off at wien tail (short $\lambda$)
• slow decrease at rayleigh jeans tails (long $\lambda$)
• higher temperature objects will have higher $B_{\lambda }$ at all $\lambda$
• peak shifts to red end as temperature decreases

wien's law

• gives the peak wavelength for any given temperature:

• wien's constant $=2.9\times {10}^{-3}mK$

• eg: what is the peak wavelength for emission from the earth?

  • $T=290K$
  $${\lambda }_{max}=\frac{2.9\times {10}^{-3}}{290}={10}^{-5}m=1\mu m$$

stefan-boltzmann law

• total power emitted per unit area ($J$) is given by:

where, $\sigma =5.67\times {10}^{-8}W{m}^{-2}{K}^{-4}:$ stefan-boltzmann constant

• eg: what is the power emitted by a person?
  • $T=310K$, $S.A.=2m^2$
  $$P=5.67\times {10}^{-8}\times (310{)}^4\times 2\approx 1000W$$