2. 2.2 Thermische Hohlraumstrahlung und Energiequantisierung
Spektrum der Hohlraumstrahlung: Experimentelle Ergebnisse
Spektrum bei kleinen Frequenzen:
"Rayleigh-Jeans"
Spektrum bei kleinen Frequenzen:
"Wien"
Wellenlänge maximaler Intensität hängt von der Temperatur ab:
"Wien'sches Verschiebungsgesetz"
Gesamte Strahlungsleistung:
"Stephan Boltzmann Gesetz"

3. The color of a black-body changes as a function of its temperature.
Hotter temperatures appear blue, cooler appear red.
This is described by Wien’s Law: l~1/T
We make use of this effect to indirectly measure the temperature of many objects.

4. Thermodynamics – I Thermodynamics Entropy
Scientists of the 19th century and earlier developed a very general theory about how changes in the energy of a system are related to changes in macroscopic quantities such as volume and entropy.
Entropy
Entropy S is a measure of the disorder of a system. If a system can be in any of W different configurations, its entropy is defined by
S = k ln W
k = x J / K is Boltzmann’s constant.

5. Black-body Radiation – III
Gustav Kirchhoff
In 1860, Gustav Kirchhoff challenged scientists to derive the functional form of the spectral density.

6. The Quantum – II An Act Of Desperation
Planck showed that the entropy per oscillator has the form
He used ST = k ln W, the total entropy of the oscillators, and the following model
M indistinguishable quanta, each with energy e
distributed over N oscillators, each of which can absorb or emit zero or more quanta.
The average energy per oscillator is E = M e / N
S, the entropy per oscillator, is = ST / N

7. The Quantum – III Planck’s Model
The number of ways of distributing M indistinguishable items (quanta) amongst N boxes (oscillators) is
To see this, represent the N boxes by N-1 indistinguishable partitions. In total we have M+N-1 objects. The number of ways to arrange them is
(M+N-1)!.
But of these arrangements M! x (N-1)! are indistinguishable, so we must divide by that number.

8. The Quantum – IV The Reluctant Revolutionary
Planck then used the thermodynamic relation 1/T = ∂S/∂E to derive the entropy per oscillator, starting with his successful formula for the black-body spectral density
When he compared the two entropy formulae, one derived from his model and the other from his formula for r(n,T) he found that they would agree only if the following were true
Thus did this reluctant revolutionary start, in an “act of desperation,” the quantum revolution

9. Summary Catastrophe The Quantum
Rigorous application of thermodynamics and the laws of Newton and Maxwell by Lord Rayleigh led to an absurd prediction:
A hot oven should emit an infinite amount of energy
The Quantum
In, what Planck described as an “act of desperation”, he derived the correct formula for the black-body spectral density that required energy changes to occur in discrete amounts given by E = h n
Thus was born the quantum.

10. Problem
Using Planck’s model, derive Planck’s formula for the entropy per oscillator
Use 1/T = ∂S/∂E to show that the average energy per oscillator is given by
E = e /(ee/kT - 1)
Hint:
for large N, ln N! ~ N ln N - N

11. Temperature and Light Hot objects give off light
Temperature is a measure of how fast the atoms/molecules are moving
hot atoms move faster than cooler atoms
faster movement means more collisions
Collisions of atoms can convert energy to light
This is how an incandescent
light bulb glows

12. Temperature and Light Hotter objects give off more light L  T4
e.g. if you double an object’s temperature, the luminosity goes up by a factor of 16 (24)
Hotter objects give off bluer light
  1/T
e.g. if you double an object’s temperature, the wavelength drops in half

13. Blackbody Radiation
Light radiated due to temperature, follows a pattern
blackbody radiation
all objects radiate light
This can be used to measure the surface temperature of an object
this is how we can measure the temperature of the Sun

14. we can rewrite as T = (2900 m K)/
Temperature of the Sun
We learned that   1/T
Really, it is  = (2900 m K)/T
we can rewrite as T = (2900 m K)/
m = micron = 1 x 10-6 m
K = Kelvin (a measure of temperature
K = 0 is absolute zero, the coldest temperature possible
K = 273 is the freezing point of water (32 oF)
K = 373 is the boiling point of water (212 oF)
the Sun’s light peaks at  = 0.5 m
So, T = (2900 m K)/0.5 m = 5,800 K
So the surface temperature of the Sun is 5,800 K

15. EM Radiation Spectral lines Blackbody radiation A particle and a wave
emission
absorption
pattern
atmospheric transmission
Blackbody radiation
A particle and a wave
behaves differently depending on how you “look” at it
waves
wavelength, frequency
speed – c = lf = ln
all EM radiation travels at the same speed in a vacuum
particles – photons
E = hf = hn – higher frequency means higher energy