RADIATION BASICS CLASS
NOTES FOR MECHANICAL ENGINEERING
Radiation is very common. It comes from each and every
body. Each type of radiation is harmful to all types of living
beings. Some of these radiations have provided many
types of ease in life. Laws of radiation make the study
of radiation simple and easy. Radiations of all types are harmful.
More energetic radiations are more harmful.
Time of exposure also plays an important role.
These help in developing many types of modern
domestic, commercial and industrial equipment’s.
Radiation is heat transfer by electromagnetic rays (EMR). EMR does not need a medium. These radiations are SELF-PROPAGATING WAVES. These travel in vacuum or in a matter medium. All the radiations move with the velocity of light 3 x 108 m/s .Most of these are invisible. Order of decreasing energy is gamma rays, X-rays, Ultra Violet rays, visible rays, Infra-red rays and Radio waves. EMR are visible only in the range of wavelength of 0.38 to 0.75 microns. Vibration and rotational motion of molecules, atoms, protons and electrons cause radiations.
These EMR has oscillating vertical electric field and horizontal magnetic field. These cause motion. Energy propagation is perpendicular to the direction of EMR. These carry energy away from the emitting object. The radiation energy travels outward in straight lines in all directions from its source. These are measurable and comparable. Each type of EMR has a wavelength range (say, Gamma rays 10-6 to 10-5 microns). For each wavelength, there is an EMR. EMR in gamma rays band has different wavelengths, different frequencies, and different energies. In each type of radiations, there are numerous rays. Bodies at higher temperature emit more radiations and of more types.
STEFAN BOLTZMANN EQUATION
A Body internal energy changes giving out radiations. Stefan- Boltzmann Law govern radiations coming out hot bodies.
Heat flux=σ T4 W/m2.
Radiated energy is in the form of photons. Unit of energy of each EMR is 1 photon. 1 photon=hν=1e=mc2 and wavelength λ=c/ν=h/m c, Where h is Planck’s constant=6.26 x 10-34J s and m is mass. 1 photon does not indicate a certain fixed energy. Energy of photons of gamma ray & X-rays is different. Even photons of any EMR contain different energy because of different wavelengths in any particular type of rays. These photons move randomly with random phase and random frequency. When these photons reach another surface, these are partially or fully absorbed, reflected & transmitted.
1. FACTS ABOUT RADIATIONS
Plastic is opaque to visible light.
Plastic is transparent to infrared radiations.
Dark glasses are opaque to infrared radiations.
Dark glasses are transparent to visible light.
Both ionizing and non-ionizing radiations can be harmful to organism. It can change the natural environment.
2. RADIO WAVES
Radio waves with λ= 3000 to 300 m,
TV waves with λ= 300 m to 30 m,
FM waves with λ = 30 m to 3 m,
mobile phone waves with λ= 3m to 30 cm,
Microwaves with λ = 30 cm to 0.3 cm,
Waves from remote with λ < 0.3 cm. These are, also, called shorter infrared radiations.
3. HUMAN BODY RADIATIONS
Body skin temperature is about 330C,
Clothing reduces the surface temperature to about 280C,
Ambient temperature is 200C,
net radiative loss from human body is 104 J/s=9 x 106 J/day=9 MJ/day=2400 kcal/day,
Area of the body is 2m2.
4. SUN RADITIONS
Sun temperature at the outer surface= 5900 K,
temperature at center of the sun= few million oC,
Total energy radiated from the outer surface of the sun= 3.86 x 1026 Watts,
Solar constant = 1367 W/m2, it is flux reaching the outer surface of earth atmosphere.
Heat flux = q· ”=σ T4 = 5.6703 x 10-8 x 58004=6.42 x 107 W/m2,
Bright sunshine gives an irradiance of just over 1kW/m2 at sea level, Out of this is 525 W/m2 is infrared radiation, 443 W/m2 is visible light, 32 W/m2 is ultraviolet radiations.
5. DIFFUSED SURFACE
It is a surface from which directions of emitted, reflected and incident radiations are unknown or is unpredictable.
6. THERMAL RADIANTIONS ENERGY
Infrared radiations energy is thermal radiant energy.
7. DRIVING FORCE IN RADIATION
Driving force in radiation is (T14–T24) and not just the temperature difference as in conduction and convection.
8. TEMPERATURE LIMIT FOR GIVING RADIATIONS
A body at a temperature above 0 K gives radiations.
9. CONCEPT OF A BLACK BODY
In practice, a hollow enclosure having a small hole approximates a black body.
The enclosure absorb all the radiations entering the hole. Radiations coming out the small hole is negligible. A small hole becomes a “black body”.
10. Black body radiation
Radiation from a black surface depends only on temperature and does not depend on the nature of the surface. At lower temperature, radiations are less. With increasing temperature, amount of radiations increase. The quantity of radiations with small energy decrease. A BLACK BODY APPEARS ABSOLUTELY BLACK AS IT WOULD NOT REFLECT AND WOULD NOT TRANSMIT ANY LIGHT FALLING ON IT.
11. Spectral emissive power and its relation with total emissive power?
Spectral emissive power is the emissive power for one wavelength only. It varies with wavelength.
It is rate of radiated energy per unit surface area per unit wavelength. Express it as W/m2m wavelength.
Relation of total emissive power is
E total = Integral(o to infinity) Ebλ dλ W/m2
Ebλ is the monochromatic emissive power of a black surface at wavelength ‘λ’.
12. Variation of emissivity ‘Є’
Є of a grey body is constant at a certain temperature. Emissivity of a grey surface is independent of wavelength. Whereas Є of a real surface varies with wavelength.
PLANCK’S LAW OF MONOCHROMATIC EMISSIVE POWER
It is relation for the monochromatic emissive power of a black body for one particular wavelength λ. Mathematically the relation is
(Eλ)b=c1λ-5/ (ec2/λT –1) W/m2
Where λ is any wavelength
Constants are c1 and c2
c1 =0.374 x 10-15 Jm2/s
c2=1.4388 x 10-2 m K
RAYLEIGH LAW OF MONOCHROMATIC EMISSIVE POWER
This law is an approximate Planck’s Law for monochromatic emissive power (radiation Flux) and is used only for long wavelengths (when λT >8x 105 μmK)
Use approximate law because it is much simpler. There is a maximum error of 1 % in the value of emissive power for longer wavelengths. This error being quite small and is negligible.
WEIN’S APPROXIMATE LAWS FOR MONOCHROMATIC RADIATIONS
(i) Monochromatic emissive power ; Applicable only for shorter wavelengths (λmT < 2900 μmK)
Use it because it is much simpler. There is a maximum error of 1 % in the value of emissive power for shorter wavelengths. This error being quite small and is negligible.
STEFAN-BOLTZMANN LAW COMES FROM PLANK’S LAW.
WEIN’S DISPLACEMENT LAW ALSO COMES FROM PLANCK’S LAW.
Planck Law is for black body for one wave length. Two laws derived from Planck Law are very useful. These are Stefan-Boltzmann Law and Wein’s Displacement Law.
FIRST IS STEFAN’S BOLTZMANN LAW
It gives the total emissive power (heat flux) due to all wavelengths. It is for a black body and the equation is
Eb=∫Ebλ dλ =σb T4 W/m2
This Eb is the emissive power (heat flux) of a black body
Where Stefan’s -Boltzmann Constant is σb = 5.67 x 10-8 W/m2K4
T is the absolute temperature in K = 273+ 0C
Emissive power (heat flux) for a grey body
Where Eg is the emissive power of a grey (real) body
Є is the emissivity of a grey body and has no units.
It is less than or equal to 1 i.e. Є≤1.
Further, Є σb is called radiation constant =5.7 for a black body, =5.16 for lamp black, =5.13 for glass, =1.19 for silver, =0.119 for polished copper
SECOND IS WIEN’S DISPLACEMENT LAW
As temperature increases, the wavelength for maximum emissive power shifts towards left in the Fig. shown below. Mathematically Wein’s Displacement Law gives λmT = 2900 µmK
Observations from the Fig. for Wien’s Displacement Law
Fig. Wien’s law gives the shift of the peak value.
(i) At a certain value of λ, Eλb increases with the increase of temperature
(ii) Further, at a certain temperature , , Eλb increases with the decrease of λ
(iii) For temperatures below 800 K, radiations are infrared radiations.
KIRCHHOFF’S LAWS OF RADIATIONS
There are two Kirchhoff’s Laws.
First Kirchhoff’s law
It states that the ratio of emissive power to absorptivity of a grey body is constant. It is equal to the emissive power of a black body at the same temperature.
(E/α)T= (E1/α1)T= (E2/ α2)T = (Eb)T
Second Kirchhoff’s Law
The absorptivity of a real body is equal to its emissivity under identical temperature and identical wavelength.
α 1 = Є1
Then firstly Eb=σbT4
Secondly Eg=Є σbT4
Which gives Є=Eg/Eb
Therefore, Є= α
LAMBERT’S COSINE LAW
Fig. Lambert’s Cosine Law
Iϴ=In cosϴ Where ϴ is the angle between the surface normal and the viewer direction.
Where Iϴ= Intensity at angle ϴ
In = Intensity in the normal direction
13. Surface resistance and space resistance
Fig. Space & Surface Resistances
Surface resistance is the resistance in radiation for a single radiating body
Q net=from a single radiating body = (Eb –J)/ [(1—Є)/AЄ]
Here (1—Є)/AЄ is the surface resistance
Space resistance is the resistance of the space between two radiating surfaces.
Q net=between two radiating bodies = (Eb –J)/ A1F12
Space resistance = 1/A1F12
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