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Wein’s Law, also known as Wien’s Displacement Law, is a fundamental principle in the field of thermal radiation and blackbody physics. Formulated by William Wien in 1893, this law describes the relationship between the temperature of a blackbody and the wavelength at which it emits radiation most intensely. According to Wein’s Law, as the temperature of a blackbody increases, the peak wavelength of its emitted radiation shifts to shorter wavelengths.
This principle is pivotal in understanding various astrophysical phenomena, the behavior of stars, and applications in thermal imaging and infrared technology. Through Wein’s Law, we gain critical insights into the thermal properties and the emission spectra of objects based on their temperatures.
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What is Wein’s Displacement Law?
Wein’s Law, also called Wien’s Displacement Law, is named after the German physicist William Wien for his important work in explaining blackbody radiation. This law shows the connection between the wavelength of light with the highest intensity and the object’s absolute temperature.
Wien’s Displacement Law states that the peak wavelength of radiation emitted by a black body is inversely proportional to its temperature. This means that as the temperature increases, the peak wavelength decreases. This shift in peak wavelength is due to the Planck radiation law, which describes the intensity of black-body radiation as a function of wavelength for a given temperature.
Wien’s Law helps us understand that objects at different temperatures emit light at different wavelengths. Hotter objects emit light at shorter wavelengths, which appears blue, while cooler objects emit light at longer wavelengths, which appears red.
Named after William Wien, who formulated it in 1893, the law was derived from his studies on the adiabatic expansion of a cavity containing light waves in thermal equilibrium. By applying Doppler’s principle, Wien showed how the energy of light changes with frequency during expansion or contraction. He used Boltzmann’s thermodynamic principles to theoretically deduce this important law.
Wein’s Displacement Law Formula
Wien’s Displacement Law can be written as:
λmaxT=b
Here,
- λmax is the wavelength at which the blackbody emits the most radiation.
- b is Wien’s constant, which equals 2.897×10−3 meters kelvin (m·K).
Also Check: Kirchoff’s Law
Wein’s Displacement Law Derivation
William Wien used thermodynamics to explain how the distribution of wavelengths relates to the energies emitted by radiation, a principle known as Wien’s Law of Distribution. According to Wien’s law, the energy distribution varies as a function of λ⁻⁵.
For shorter wavelengths (λ), the exponential factor becomes large, contributing more and overcoming the λ⁻⁵ factor, meaning that at shorter wavelengths, the energy (E) increases with λ. Conversely, for higher wavelengths, the exponential factor is very small, making λ⁻⁵ dominant, so E decreases at higher λ.
Initially, Wien’s law seemed accurate for explaining the blackbody radiation curve. However, when comparing the curve plotted by Wien’s law with experimental data, we see that while Wien’s law fits well at shorter wavelengths, it diverges at longer wavelengths. This discrepancy indicates an error in Wien’s theoretical distribution, too significant to be attributed to experimental uncertainties, highlighting a flaw in the theory. Wien could neither explain this failure nor provide a better theory.
Despite its limitations, Wien’s law allows us to deduce the maximum spectral emissive power’s dependence on temperature. According to Wien’s displacement law, at λ = λₘ, we have λₘT = b.
Where:
- λₘ is the maximum wavelength corresponding to maximum intensity,
- T is the absolute temperature,
- b is Wien’s constant, valued at approximately 2.88 x 10⁻³ m-K or 0.288 cm-K.
Wien’s displacement law and the Wien’s displacement law formula provide important insights, even though the law is not perfect for all conditions.
Also Check: Ohm’s Law
Importance of Weins Law
Wien’s displacement law class 11 helps us determine the temperature of astronomical objects. This law is also used in designing remote sensors. Other uses of Wien’s displacement law include:
- Incandescent Bulb Light: As the temperature of the filament decreases, the light shifts to longer wavelengths, making it appear redder.
- Temperature of the Sun: We can study the sun’s peak emission at around 500 nm, which is in the green spectrum and visible to the human eye.
In class 11, understanding Wien’s displacement law helps students learn how the temperature of an object affects the wavelength of the light it emits.
Application of Wein’s Law
Here are some Wein’s Law Application:
- Wood Fire Radiation:
- A wood fire at 1500 K emits peak radiation at 2000 nm.
- Most of this radiation is invisible to the human eye, which is why bonfires provide heat but are not very bright.
- Incandescent Light Bulb:
- Using a dimmer on an incandescent bulb changes the filament’s temperature.
- As the filament cools, the light shifts to longer wavelengths, appearing redder and dimmer.
- This demonstrates Wien’s Displacement Law.
- Sun’s Radiation:
- The sun’s surface temperature is about 5700 K.
- Wien’s Displacement Law indicates the peak radiation is at 500 nm, in the green part of the visible spectrum.
- This wavelength is highly sensitive to human eyes.
- Mammal Infrared Emission:
- Mammals with skin temperatures around 300 K emit peak radiation in the far infrared, around 10 micrometres.
- Pit viper snakes and passive infrared cameras detect this range.
- Heating Metal:
- A heated metal object first becomes “red hot.”
- As it heats more, it changes from red to orange to yellow, and finally to white, showing the shift to shorter wavelengths as it gets hotter.
- Star Emission:
- Many stars do not emit most of their light in the visible range.
- For example, Rigel, a hot supergiant, emits 60% of its light in the ultraviolet.
- Betelgeuse, a cool supergiant, emits 85% of its light in the infrared.
- Wein’s Displacement Law Formula:
- The formula relates the temperature of an object to the peak wavelength of its emitted radiation.
- It is crucial for understanding various phenomena in fields like astrophysics and thermal imaging.
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FAQs on Wein’s Displacement Law
What is Wien’s Constant?
Wien’s constant (b) is a physical constant that defines the relationship between the absolute temperature of a blackbody and the wavelength at which it emits radiation most intensely. Denoted by b, this constant helps determine the peak wavelength of radiation for a given temperature. As the temperature of the blackbody increases, the wavelength of maximum emission becomes shorter.
What is Black Body Radiation?
Black body radiation refers to the energy emitted by a surface at a specific wavelength, which depends on the surface’s temperature, composition, and condition. A blackbody is an idealized physical object that emits the maximum possible thermal radiation for its absolute temperature. In thermal equilibrium, a blackbody has an emissivity of ε = 1.0, meaning it absorbs and emits all incident electromagnetic energy perfectly. Real-world objects, known as gray bodies, have emissivities less than 1.0 and emit less radiation compared to a blackbody. At room temperature, a blackbody emits approximately 448 watts per square meter of thermal radiation.
Why do Things Emit Light When Heated?
Objects emit light when heated due to a process known as blackbody radiation. When an object is heated, its particles, including electrons, become more agitated, causing collisions and changes in motion. This agitation results in the emission of electromagnetic radiation, transferring energy away from the object. As the temperature rises, the atoms vibrate, and electrons move between higher and lower energy states, causing the object to glow. This phenomenon is called incandescence.
What is Wien's Displacement Law Used For?
Wien's Displacement Law is a useful formula for determining the temperature of stars. It is based on the principle that hotter objects emit more radiation at higher frequencies compared to cooler objects. By using Wien’s Displacement Law formula, scientists can calculate the temperature of a star by observing the peak wavelength of its emitted radiation.
Why is it Called Wien's Displacement Law?
Wien's Displacement Law is named so because it describes how the peak wavelength of radiation (λm) shifts based on the temperature of the blackbody. As the temperature increases, λm moves towards the shorter wavelengths (higher end of the spectrum), and as the temperature decreases, λm shifts towards the longer wavelengths (lower end of the spectrum). This shifting or displacement of the peak wavelength with temperature changes is why it is called Wien's Displacement Law.
