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