Temperature and Light

1
Temperature and Light

• Equipartition Theorem Typical energy of atom
  or photon is E kT where k Boltzmanns
  constant 8.6 x 10-5 eV/K
• Wiens law lmaxT 2.9x10-3 m- K gt peak
  wavelength varies inversely with T
• Range of T from a few degrees (outer space) gt
  mm mwave to 10,000º or more gt 100 or less nm
  visible into UV for hottest stars
• Einstein Equipartition E hf hc/l kTgt
  lT hc/k lT (4.1x10-15 eV-s)(3x108
  m/s)/(8.6x10-5 eV/K)
• .0143 m-K 14.3x10-3 m-K (in the
  park!!)
• Molecular speeds from equipartition, m
  molecules mass

2
Some Reference Temperatures part II C are 300
lower F are twice as big

• T (K) kT (eV) lmax
  comment
• 3 .25 meV 1 mm mwave
  night sky temp
• 300 1/40 10,000 nm far IR FIR
  room temp
• 500 .04 For 1H, vrms 3.5 km/s
  Sn melts
• 1200 .1 2400 nm IR Ag
  melts red
• 1800 .15 1600 nm NIR Fe melts,
  Bi boils orange-yellow
• 3000 .2 1000 nm NIR W melts
  Fe boils yellow
• 6000 .4 500 nm vis W boils
  suns temp yellow-white
• 50,000 5 58 nm UV flame plasma
  temp blue-white

Note that kT, the average energy, is about 1/5
the energy of the peak position as given by the
Wien law and Einstein photon
3
Edmund Halley (1718) discovered that some stars
exhibit proper motion
4
Fig.16.02b
The fastest-moving star Barnards Star 4 in
only 22 earth years!!
Willam Herschel (1783) discovered that the sun is
moving in the direction of Hercules -- called the
apex direction
5
Stellar Apparent Magnitude is a measure of
Brightness

• Hipparchus 1st magnitude brightest, 6th
  magnitude dimmest
• in terms of actual received energy, also called
  brightness, 6th magnitude put out 100 times less
  energy than 1st magnitude (Herschel), by using
  variable aperture (objective diameter) telescope
  clever guy!!
• The magnitude scale is actually a logarithmic
  scale!! Cool!!
• since a decrease by 5 magnitudes ? 100 times
  increase in E
• a decrease by one magnitude gives 5?100 2.512
  times increase
• for two stars of brightness b1 and b2, where b
  is a direct measure of the energy reaching the
  eye
• and suppose these two stars are of apparent
  magnitude m1 , m2

6
Some Examples

• brightest star is Sirius m - 1.4
• consider star X with m 0

• so Sirius is 3.6 times brighter than X
• your eye catches 3.6 times as many Watts from S
  as from X
• Sun m -26.5
• Full Moon m -12.5
• sun puts out 2.514 3.7 x 105 times full moon
  power
• dimmest in decent Wells telescope m 12
• dimmest for Hubble m 29