16. Black body radiation.

Question 1

Define **black body **

Answer 1

a theoretical body that is a perfect absorber (and emitter), absorbing 100% of all radiation → no reflection

Question 2

Define black body (= thermal) radiation and relate 4 laws to it

Answer 2

EM radiation that is emitted from all materials due to internal vibrations of molecules if: T > 0 K.

Heat exchange between body₁ and body₂ if: T₁ > T₂

Laws:

• Kirchhoff’s law
• Stefan-Boltzmann law
• Wien’s displacement law
• Planck’s law of radiation

Question 3

Describe Kirchhoff’s law and give its formula

Answer 3

objects that emit thermal radiation are also efficient absorbers of the same radiation (emission = absorption).

_Therefore: _

M_λi/α_λi=M_λj/α_λj

• M = spectral emissive power
• α = μ = absorption/attenuation coefficient

⇒ **α_λblackbody = 1 **

Depends on:

• material of absorber
• photon energy of radiation
• density of the absorber

Question 4

Describe the Stefan-Boltzmann law by reference of a diagram

Answer 4

Gives the total energy being emitted at all wavelengths by the blackbody which is the area under the Planck’s law curve. This law explains the growth in height of the curve as the temperature increases.

Therefore:

M_blackbody(T) = σ * T⁴

• σ = Stefan-Boltzmann constant
• M_blackbody = total emissive power, area under the curve

Question 5

Describe Wien’s displacement law by reference of a diagram

Answer 5

States that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck’s radiation law which describes the spectral brightness of black body radiation as a function of wavelength at any given temperature.

Therefore:

λ_max * T = const.

→ if λ or T increase the other factor decreases

Question 6

Describe Planck’s law of radiation

Answer 6

Explains the frequency distribution of black body radiation in thermal equilibrium at a definite temperature: the radiant energy can exist only in discrete quanta which is proportional to the frequency.
Describes the relationship between energy and wavelength.

Therefore:

E = h * f

• h = Planck’s constant
• f = frequency (=1/λ)

Question 7

Name some applications of black body radiation

Answer 7

• thermography: IR-vision, airport thermography
• infradiagnostics: breast screening, inflammation, chronic muscoskeletal stress