Just basic info regarding radiation laws. Hope it helps you. Feel free to use and copy it. Thank you

1. RADIATION LAWS
Himanjali Mylapalli
319106715047
geo_-informatics 3/4

2. STEFAN BOLTZMANN
LAW

3. What is Stefan Boltzmann Law?
◦ According to Stefan Boltzmann law, the amount of radiation emitted per unit time from an area
A of a black body at absolute temperature T is directly proportional to the fourth power of the
temperature.
u/A = σT4 . . . . . . (1)
◦ where σ is Stefan’s constant = 5.67 × 10-8 W/m2 k4
◦ A body that is not a black body absorbs and hence emit less radiation, given by equation (1)
For such a body, u = e σ AT4 . . . . . . . (2)
◦ where e = emissivity (which is equal to absorptive power) which lies between 0 to 1.
◦ With the surroundings of temperature T0, net energy radiated by an area A per unit time.
Δu = u – uo = eσA [T4 – T0
4] . . . . . . (3)

4. Derivation of Stefan Boltzmann Law
◦ The total power radiated per unit area over all wavelengths of a black body can be obtained by
integrating Plank’s radiation formula. Thus, the radiated power per unit area as a function
of wavelength is:
◦ Where,
ⅆ𝑃
ⅆ𝜆
×
1
𝐴
=
2𝜋ℎ𝐶2
ⅇ
ℎ𝐶
𝜆𝑘𝑇
−1
𝜆5
• P is Power radiated.
• A is the surface area of a blackbody.
• λ is the wavelength of emitted radiation.
• h is Planck’s constant
• c is the velocity of light
• k is Boltzmann’s constant
• T is temperature.

5. Graphical
representation
Stefan–Boltzmann law:
power radiated by a
greybody with different
emissivities.

6. EXAMPLES OF STEFAN-
BOLTZMANN LAW

7. Calculating Radius of Stars
◦ To calculate the radius of a star, its
luminosity is taken into
consideration. The luminosity is the
total power discharged by the star in
space. It depends on two factors, i.e.,
the temperature and surface area. The
relationship between the temperature
of an object, the surface area of the
body, and the rate of radiation
discharge is given by the Stephan-
Boltzmann law. Hence, it can be used
to calculate the radius of a star.

8. Heating Iron Rod
◦ When an iron rod is heated at one end, the
heat tends to spread and reach the opposite
end of the rod after some time. One of the
common misinterpretations is that the
energy transfer only takes place from the hot
end of the rod to the cold end of the rod;
however, the truth is that both the cold and
hot ends of the rod exhibit thermal
radiations in the environment. The
difference is that the hot object radiates
more than the colder one. Therefore, the net
flow of heat is from the hot end to the cold
end. This is one of the finest examples that
effectively demonstrates Stephan-Boltzmann
law in real life.

9. Sparklers
◦ The sparklers make use of the
Stephan-Boltzmann law to emit
glittery chemical particles in the
environment. When a firecracker or a
sparkler is lit, it undergoes a
significant increase in temperature.
According to the Stephan-Boltzmann
law, the temperature of the object is
proportional to the energy radiated by
it, which is why the sparkler appears
less shiny in the beginning and gets
lustrous afterwards.

10. Bonfire
◦ A bonfire is often used during winters
to keep the surroundings warm. The
warmth produced by the bonfire can
be easily felt from afar. This
effectively makes use of the Stephan-
Boltzmann law because the heat
energy is emitted in the surroundings
in the form of radiations.

11. WIEN’S LAW

12. What is Wien’s law?
◦ Wien’s law or Wien’s displacement law, named after Wilhelm Wien was derived in the
year 1893 which states that black body radiation has different peaks of temperature at
wavelengths that are inversely proportional to temperatures.
◦ Mathematical representation of the law: 𝜆𝑀𝑎𝑥 =
𝑏
𝑇
◦ where,
b is the Wien’s displacement constant = 2.8977*103 m.K
◦ T is the temperature in kelvins

13. Wien’s constant: b (Wien’s displacement
constant)
◦ Physical constant defining the relationship between
the thermodynamic temperature of the black body and the
wavelength is known as Wien’s constant. It is a product of
temperature and wavelength of the black body which grows
shorter as the wavelength reaches a maximum with
temperature.

14. Graphical
representation
Blackbody spectra for three
different temperatures,
3000K (red), 4000K (green)
and 5000K (blue). Notice the
wavelength of the peak of
each curves moves as the
temperature changes. This
is Wien’s displacement law.
The x-axis is in nanometres,
on this scale the visible part
of the spectrum is from
about 400 to 700 nm.

15. Daily life applications of wien’s law
◦ Incandescent bulb light- As the filament's temperature drops,
wavelengths lengthen, making the light look redder.
◦ The temperature of the sun - With a wavelength of 500 nm in
the green spectrum, which is in the human eye's sensitive range, one
may analyze the sun's peak emission per nanometres.