Optically Thick Case
But what if absorption occours?
But what if it gets very thick?
Then dIn = 0
Let us look at this more closely.
Consider the particles doing the absorbing and emitting.
Take two states upper, U, and lower, L.
Separate them by EU - EL = hn
Then Boltzman tells us:
also, in equilibrium
AUL = spontaneous emission
InBUL = stimulated emission
NLBLUIn = absorption
let T --> infinity, therefore I --> infinity
So in general, in equilibrium
Can be shown using box normalization and quantum mechanics that (in most circustances)
Blackbody radiation erg cm-2 s-1 Hz-1 st
Wien Law A*K
Remember, sun: T=5000lm=5000 lT = 25*106
Next look at lown end hn << kT
Cant measure T if Area unknown very inconvient if hn = kT region hidden
Finally -- total emission
From a flat dA
Radiation from a charge
Sun is a star
Star is a ball of gas with an energy source in the middle
Nuclear1MeV per particle instead of 2eV
E = 5 * 105 * 4 * 1045 = 2 * 1051 ergs
t= 15 * 109 years -- very close to correct!
What is the theral timescale of the Sun?
Thermal content at core 106K
Takes 106 years to change significantly
Lets make a star
Ball of gas at mass M
For a few thousand years chemical processes have an effect (very short time)
Gravity holds it together
Thermal Pressure holds it up
Balance the two and you have a star
P = nkT ideal gas law
RT=1.5*1018 cm deg
Chemical energy dissipates 1000 years
Gravitational energy dissipates in 3*107 years
Keeps contracting until nuclear burning sets in at T=15 million
Equilibrium is achieved
If R decreases then T increases
If T increases L increases
If L increases T increases more
If T increases R increases
Stable equilibrium is achieved