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Blackbody radiation is emitted by an ideal body that allows the entire radiation to pass through itself and absorbs the energy without reflecting. Blackbody radiation is usually referred to the spectrum of light that is emitted by a heated object. This property is implied for a blackbody in all corresponding wavelengths and angles of incidences of radiation. Hence, the blackbody is an ideal absorber of incident radiation.
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Key Terms: Blackbody Radiation, Planck’s Law, Stefan Boltzmann Law, Wien's Displacement Law, Incident Radiation, Wavelength, Light
What is Blackbody Radiation?
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Blackbody radiation is referred to the spectrum of light that is emitted by a heated object. For a body to stay in a thermal equilibrium state, it must emit radiation equal to the amount of the radiation it absorbs.
The body must act as a good absorber and a good emitter at the same time at an equal rate. The radiation emitted from the blackbody is known as Blackbody Radiation. These emitted electromagnetic waves can absorb waves of all frequencies.
Blackbody is referred to as a standard to compare with the absorption of real bodies. Blackbody is important for the study of thermal radiation theory and practice. Through this, the transfer of electromagnetic radiation and thermal radiation in all wavelength bands can be studied and analyzed.
Characteristics of Black Body Radiation
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Many chemists have studied and expressed the characteristics of the Blackbody in the form of three laws. The three laws are as follows:
- Wien's Displacement Law
- Planck’s Law
- Stefan-Boltzmann Law
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What is Wien’s Displacement Law?
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Wien’s Displacement Law states that the blackbody radiation curve for different temperatures will peak at different wavelengths and is inversely proportional to the wavelengths. This law was attained by Wilhelm Wein.
| λ = b/T |
Where
- λ = Wavelength peak
- b = constant of proportionality = 2.8977 × 10^3 m.K
- T = Absolute Temperature
This law explains the absolute relationship between temperature and wavelengths of the bodies from the curve. It can be observed that the hotter objects with more temperature emit radiations of shorter wavelength and appear in blue colour. While the objects with less temperature emit radiations of longer wavelength and appear in reddish colour.
Day-to-Day Applications of Wien's Displacement Law
 Application of Wien's Displacement Law
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What is Planck’s Law?
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Planck's law was derived by Max Planck. A blackbody in a thermal equilibrium state at a given temperature T emits electromagnetic radiations. The spectral density of these electromagnetic waves can be calculated and determined using Planck’s Law.
Where,
- Eλ = Wavelength
- h = Planck’s Constant
- c = Speed of light
- K = Boltzmann’s Constant
- T = Absolute temperature
When a blackbody is at a lower temperature most of the radiation is in the infrared region of the electromagnetic spectrum. While the temperature is higher, the radiated energy increases and thus the emitted spectrum reduces to shorter wavelengths. At this time some of the radiation will be emitted in the form of visible light.
What is Stefan Boltzmann Law?
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Stefan Boltzmann's Law states that total energy emitted is proportional to the fourth power of absolute temperature. Austrian Physicist Josef Stefan derived this law in the year 1879.
| E ∝ T4 |
Where
- E = Total energy emitted or radiant heat power
- T = Absolute temperature
Stefan Boltzmann law
Using this law the amount of energy emitted by the blackbody can be determined. With the increase in temperature the total radiated energy also increases. Then the object glows brighter than normal. Besides, the heat radiated by Earth into the atmosphere can be predicted using this law. It describes the amount of energy or power emitted by the sun.
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Things To Remember based on Blackbody Radiation
- Blackbody is an ideal body that allows the entire radiation to pass through itself and absorbs the energy without reflecting.
- A blackbody is explained by Wien's Displacement Law, Planck’s Law, Stefan-Boltzmann Law
- A black body in a thermal equilibrium state at a given temperature T emits electromagnetic radiations.
- When there is an increase in temperature the total radiated energy also increases and the object glows brighter than normal.
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Sample Questions based on Blackbody Radiation
Ques. Find the peak wavelength of the blackbody black body radiation emitted by:
i)The Sun (2000 K)
i)The tungsten of a light bulb at 3000 K (3 marks)
Ans.
- The sun (2000 K)
By Wein’s Displacement law
λmax = 2.898 × 10^-3 m K/ 2000K
= 1.4 μm
So infrared zone
- The tungsten of a light bulb at 3000 K
λmax = 2.898 × 10^-3 m K/ 5800K
= 0.5 μm
So Yellow-green zone
Ques. What are the applications of black body radiation? (3 marks)
Ans. The blackbodies are used for lighting, heating, security, thermal imaging, as well as testing and measurement applications. Planck’s Law of radiation can be used to determine the intensity of energy at a particular temperature and wavelength. Also in day to day Applications, the black body is used in solar cookers.
Astronomers have discovered that the objects and astronomical sources are black bodies. The Cosmic Microwave Background, relic radiation from the Big bang represent almost a perfect black body.
The temperature and wavelength of an object that emits the majority of the radiation can be expressed as λmax × T = 2.898 × 10^-3 mK. This is Wien's Displacement Law. To determine the temperature of stars and other cosmic objects this formula is used by astronomers. Moreover, the colour of their light is also identified by measuring the wavelength.
Ques. The total energy of a black body radiation source is collected for five minutes and used to heat water. The temperature of the water increases from 10.0oC to 11.0oC. The absolute temperature of the black body is doubled and its surface area is halved and the experiment is repeated for the same time. Will the temperature increase or decrease? (2 marks)
Ans. By the Stefan's Law of Radiation, the energy emitted from a black body at a temperature T and a surface area A, for a time Δt is
ΔQ = σAT^4Δt
It is given that,
A2 = 0.5 × A1
T2 = 2 × T1
ΔQ2 = σ A2 T2 ^4 =σ (0.5×A1) (2×T1)^4 = 8 σ x A1 x T1^4 = 8ΔQ1
Let the rise in temperature of the water be δT, the mass of water be m and specific heat be s
We then have,
ΔQ1=ms×1°C ----------(1)
ΔQ2=ms×δT ----------(2)
From 1 and 2 we get
1°C δ T = 8 ⇒ δT = 8°C
Thus, the temperature of water rises from 10°C to 18°C.
Ques. Is the black body radiation continuous or discontinuous? (2 marks)
Ans. The radiations emitted from the black body are discrete over the full light spectrum. These emissions from atoms have specific characteristics. Over the full spectrum, the solids emit radiation. The peak of the spectrum can be determined by the temperature of the solid. When the solid gets heated solid and interactions take place within the atoms, the emissions are produced. The atomic interactions produce vibrational modes which in result produce the spectrum of emissions. So, it emits radiations that are continuous. Perfect black body emitters produce continuous spectrums. However, when compared most of the solids are not good emitters.
In short, the black body radiation has a continuous frequency producing continuous spectrums and it only depends on the body's temperature. This is also called Planck’s Law.
Ques. What does Wien’s Law describe about the black body radiation? (2 marks)
Ans.
Wien's Law
Wien’s Displacement Law states that for different wavelengths at different temperatures, the black body radiation curve is at peaks and is inversely proportional to the wavelengths.
λ×T=b
- Using Wien's Law one the wavelength at which maximum power contribution exists can be determined. This law explains the absolute relationship between temperature and wavelengths of the bodies from the curve.
- It can be observed that the hotter objects with more temperature emit radiations of shorter wavelength and appear in blue colour. While the objects with less temperature emit radiations of longer wavelength and appear in reddish colour.
Ques. What does Stefan-Boltzmann's Law describe about the black body radiation? (2 marks)
Ans. The law states that total energy emitted is proportional to the fourth power of absolute temperature.
U= σ×A×T^4
Using this law the amount of energy emitted by the black body can be determined. With the increase in temperature the total radiated energy also increases. Then the object glows brighter than normal.
Besides, the heat radiated by Earth into the atmosphere can be predicted using this law. It describes the amount of energy or power emitted by the sun.
Ques. State a few characteristics of Black body radiation Spectra? (2 marks)
Ans. Characteristics of blackbody radiation spectra:
- The emitted power Eλ from a black body increases with the increase in temperature for every wavelength λ.
- The curve obtained from the spectrums has a characteristic form with maximum emissive power Eλ at a particular wavelength λm.
- The wavelength λm depends on the temperature T of the black body i.e. the higher the temperature, the shorter the wavelength λm.
- λmT is a constant.
- The total radiant power of a black body at the respective temperatures can be calculated with the area under each curve and is proportional to T^4. This is Stefan's Law.
Ques. What is total emissive power? (2 marks)
Ans. The total emissive power of a body at a particular temperature is defined as the total amount of radiant energy emitted per second per unit area of the surface of the body. It is represented by the symbol e.
Its SI unit is J m-2 s-1. The total emissive power of a black body is represented by the symbol E.
Ques. What is total absorption power? (1 mark)
Ans. The total absorptive power of a body is defined as the ratio of the total radiant energy absorbed by the body in a certain interval of time, to the total energy falling upon it in the same interval of time. It is represented by the symbol a.
The total absorptive power of a black body is represented by the symbol A. By definition A = 1.
Ques. Explain why a body with large reflectivity is a poor emitter. (1 mark)
Ans. According to Kirchoff’s law of black body radiation, good emitters are good absorbers and bad emitters are bad absorbers. A body with large reflectivity is a poor absorber of heat and consequently, it is also a poor emitter.
Ques. Explain why an optical pyrometer (for measuring high temperatures) calibrated for ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open but gives a correct value for the temperature when the same piece is in the furnace. (2 marks)
Ans. An optical pyrometer is based on the principle that the brightness of a glowing surface of a body depends upon its temperature. Therefore, if the temperature of the body is less than 600°C, the image formed by the optical pyrometer is not brilliant and we do not get a reliable result. It is for this reason that the pyrometer gives a very low value for the temperature of red hot iron in the open.
Ques. What is Emissivity? (1 mark)
Ans. The emissivity of a body is the ratio of the total emissive power of the body to the total emissive power of a black body. It is represented by the symbol ε. It means that ε =e/E or e=εE. For a block body, ε=1.
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