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Lecture 4: The Thermodynamic Behavior of Light and Matter
Thermodynamic Behavior of Lightthermal radiationmonochromatic specific intensity B!(T )
energy radiated per second per unit wavelength per unit solid angle, toward direction P, from a surface that has unit area in perpendicular projection to direction of emissionP
B!(T ) =2hc2
!5
1
ehc/!kT! 1
Planck’s Law
doesn’t matter what body is made of! thus, can’t know composition
uniform T, opaque source, photons scattered on way out
thermodynamic equilibrium with radiation field: T_matter = T_rad
isotropic & unpolarized
referred to as thermal or Blackbody radiation
only depends on T!
Implications: Wien’s Displacement Lawas T increases, peak of thermal radiation shifts toward shorter wavelengths (bluer)
!max = 0.29/T wavelength in cm
! T4
Implications: Stephan-Boltzmann Law as T increases, energy flux leaving blackbody surface increases
! T4
f = !T 4 where ! is the Stephan ! Boltzman constant
Sources of EM radiation
blackbody radiation (thermal)
bound-bound transitions
free-bound transitions
free-free radiation
accelerated particles (for example, in B field, synchrotron)
particle decay
The Laws of Thermodynamics
0th: heat diffuses from hot to cold
1st: heat is form of energy (important to consider for conservation of energy, quality of energy different)
*2nd: non-decreasing entropy, increasing disorder, things wear out (for example, cathedral: less info needed to specify architecture higher entropy)
3rd: absolute zero temperature
entropy is a REAL and QUANTIFIABLE quantity
Heat added = T!S
more importantly: entropy changes are not time-reversible, unlike microscopic laws of physics
statistical improbability of certain outcomes
much of history of universe is battle between gravity and 2nd law
billiard balls come to stop eventually, where did energy go?probably not reversible! information in moving cue ball flows into random jiggling of countless molecules
Statistical Mechanics (another way to treat equilibrium behavior)
W = number of microstates (where position, momentum of every particle known within quantum limits) compatible with certain macrostate (# particles in 1st, 2nd, ... bins)
given macrostate corresponds to many microstates, macrostate in thermodynamical equilibrium (relaxed) maximizes W
S = k ln(W), so macrostate in thermo equilibrium has maximum S
one microstate
which is the equilibrium situation?
which has the larger entropy?
this “ordering” can be spatial, but can also be in terms of energy (phase space)
two different macrostates, which has more microstates?
which is the equilibrium situation?
which has the larger entropy?
this “ordering” can be spatial, but can also be in terms of energy (phase space)
3 0
0 1
W = 4
which is the equilibrium situation?
which has the larger entropy?
this “ordering” can be spatial, but can also be in terms of energy (phase space)
3 0
0 1
1 1
1 1
W = ?
thermodynamics valid only for large numbers of particles (no temperature of a single atom)
particles will have distribution of energies (even though system is characterized by global properties like T), high energies are exceedingly rare
systems strive for thermodynamic equilibrium (but there are often obstacles)
Perfect Gas
particles separated beyond range of forces (colliding neutral particles)
P = nkT
E =3
2nkT 1/2 kT per degree of freedom per
particle
The Sun as a Star
f = 1.36 ! 106erg sec!1cm!2
solar constant (energy flux from sun)
r = 1AU = 1.5 ! 1013
cm
L! = f · 4!r2
= 3.90 ! 1033 erg sec!1
What effective temperature characterizes Sun’s radiation?
R! = 6.96 ! 1010
cm (how could you measure this?)
for blackbody
L! = emission per unit area of BB ! surface area
= !T4
e· 4"R
2
!
T! = (L!/!4"R2
!)1/4 = 5800K
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