Understanding Wiens Law, Methods, and Applications

Wiens Law

Learn more about Wiens law in this brief article, including how it is represented mathematically and in the formula. 

We all know that a kettle with boiling water is hotter than a bucket filled with ice cubes. This understanding comes from the general notion of heat and temperature.

Do you know what temperature and heat are? How can we differentiate these two entities? Heat and temperature are interconnected but do not mean the same thing. To understand the physical world better, it is necessary that we clearly understand the difference between heat and temperature. 

What happens when we give heat to a substance? The temperature of the substance will increase. And when we decrease the temperature, the body loses heat. The interconnectivity often leads to the false perception of heat and temperature. 

What is Wiens law?

According to Wiens law, black body radiation has various levels of wavelength with varying peak temperatures that are inversely proportional to the temperatures.

Mathematically, λ_max= b/T

Where, b = Wien’s displacement constant = 2.8977 x 10³mK, and T = temperature in Kelvins.

Alternatively, the Formula can be Written in Two Ways:

1. Frequency-dependent formula

v_max= α/h kT 

Where, k = Boltzmann constant, h = Planck constant, T = temperature in Kelvin, and α = constant whose value = 2.821.

2. From Planck Constant

 λ_max= h_c/z 1/kT = 2.8977 x 10⁶/T  nmK

Methods of Heat Transfer 

1. Conduction: What will happen if you place one end of an iron rod in a flame? The heat from the flame will eventually reach the other end of the rod. The process of heat transfer from one part of the body to the other due to temperature differences is known as conduction. Heat conduction is the time rate of heat flow at a particular temperature. 
2. Convection: Convection occurs when heat flows due to the actual motion of matter. This type of heat transfer happens only in fluids. There are two kinds of convection: natural and forced. An example of natural convection is the trade winds that blow from the northeast to the equator. Air cooling systems in our homes are a perfect example of forced convection. 
3. Radiation: How does the heat energy from the sun reaches earth? Both conduction and convection need a medium to disseminate heat. Heat transfer with the help of electromagnetic radiation is known as radiation. 

Radiation 

It is now clear that radiation does not require any medium of transfer. Before we discuss the details of radiation, we should know what electromagnetic waves are. Electromagnetic waves are waves that have oscillating electric and magnetic fields.

Like any other waves, EM waves also have different wavelengths and travel through the vacuum at the speed of light. The heat from the sun reaches the earth so fast since there is no medium present between them. 

Radiation is the transmission of heat by electromagnetic waves in space. Radiation occurs at the speed of light and is the fastest mode of heat transmission. Heat transfer through radiation will not occur until the EM waves get in contact with matter. Heat transfer occurs when the thermal energy of matter increases when EM waves come in contact. Heat transfer through radiation is a measure of the absorbance of electromagnetic waves.

All bodies, solid or liquid or gas, emit radiant energy. Thermal radiation is when a body emits radiation because of its temperature, as in the radiation from a hot iron rod or light from a filament bulb. When this thermal radiation falls on another body, based on the color of the body, it is partially absorbed and partially reflected. 

Black Body 

The black body is an ideal concept in physics. If a body, irrespective of wavelength and angle of incidence, absorbs all the electromagnetic radiation that falls on it, it is known as a black body.

The blackbodies absorb and emit radiation better than light-colored bodies. We wear white-colored clothes during summer so that they absorb the least amount of heat from the sun. However, we prefer to wear dark-colored clothes during winter.

The bottom of the cooking utensils is blackened to absorb maximum heat from the fire. All of these prove the practical applications of black bodies. 

Black Body Radiation 

The black body, to maintain equilibrium, should emit radiation that equals the amount of radiation absorbed. The radiation cast by a black body is known as black body radiation. We have understood the wavelength content of thermal radiation from the above discussion. Thermal radiation is a function of many wavelengths of varying ranges at a particular temperature. However, the energy content varies for different wavelengths.  

The figure illustrates the energy emitted by a black body per unit area per unit wavelength at different temperatures. From the graph, it is clear that,

1. The radiation emission is a continuous function of wavelength. 
2. At any specified temperature, the emitted radiation increases with an increase in wavelength, reaches a peak, and then decreases with an increase in wavelength. 
3. The emitted radiation at a specific wavelength increases with an increase in temperature. 
4.  The radiation is maximum at the short wavelength region in higher temperatures.  

Now let us look more closely into Wiens displacement law. 

From the graph, it is clear that the wavelength at which maximum radiation occurs decreases with an increase in temperature. Wiens displacement law gives the relation between this wavelength and temperature. The following equation is called Wiens law calculator.

                                 m T = constant

m = wavelength at which the energy is maximum 

T= temperature 

The constant in the Wiens law formula is Wien’s constant. Its value is 2.910^-3K. 

It is clear from the equation that the wavelength at maximum radiation is inversely proportional to the temperature. It also explains the leftward shift of the peaks as the temperature increases in a Black body spectrum. 

Uses of Wiens law Displacement 

1. It explains the change in color of an iron rod from dull red to yellow when placed in a flame. 
2. Wien displacement law helps to predict the temperature on the surface of celestial bodies like the sun and moon. 
3. Designing remote sensors. 
4. The light from incandescent bulbs appears redder when the temperature decreases.

The black body radiation does not depend on the size, shape, or nature of the material of the black body. The attempts to explain black body radiation stimulated the quantum physics revolution in the twentieth century. Wilhelm Wien is a German physicist who received the Nobel Prize in 1911 for the displacement law explaining the radiation emitted by a perfect black body. 

Drawbacks of Wiens Displacement Law 

The main limitation of the law is that it fails to explain black body radiation at longer wavelengths. Also, it is hard to obtain a continuous spectrum when the temperature decreases. 

Planck’s Law

Plank’s law was proposed in 1900 by a German physicist, Max Plank, the spectral distribution of blackbody radiation. According to Plank, the source of radiation is oscillating atoms. While Plank’s law helps to define the spectral density of radiation, Wien’s displacement law establishes a connection between peak wavelength and temperature. 

Stefan-Boltzmann law

This law establishes the relationship between the total energy emitted from a surface and the temperature. It states that the total energy emitted is proportional to the fourth power of the absolute temperature. People often confuse Stefan-Boltzmann’s law and Wien’s displacement law. The former gives the relationship between total energy emitted and temperature, while the latter relation between the highest wavelength and temperature. 

Conclusion

Heat and its transfer play a key role in many aspects of our daily life. The engineering perspective of heat gives it more importance. Civil, mechanical, and chemical engineering are closely related to the concept of heat, as a clear understanding of heat is necessary for the selection of machinery with high efficiency. Better knowledge in the conceptualization of heat has led to the discovery of many helpful inventions. 

For example, convection is the guiding principle behind ovens, electronic cooling systems, radiators, etc. The discovery of electromagnetic waves and the wave nature of atoms led to the development of a new branch in physics, Quantum mechanics. 

At the beginning of quantum mechanics, the biggest challenge in front of science was to explain the wave nature of atoms. Many scientists have devoted their studies to coming up with sufficient explanations. Black body radiation has a significant role in quantum mechanics. When Max Plank explained black body radiation using quantum mechanics, Rayleigh-Jeans and Wien explained the radiation for longer and shorter wavelengths, respectively. 

While quantum physics mainly focuses on experiments on electrons and photons, it is not limited to that realm. Quantum mechanics in the physical world will help us bridge the gap in physics and provide a clear picture of occurrences in our daily life. 

Frequently Asked Questions 

1. State Wiens displacement law.

Wiens law gives the relation between the peak wavelength and the temperature. The wavelength, m, is inversely proportional to the temperature, T. 

Wiens law formula is

                         m T = constant  

The constant in the above equation is Wien’s constant. Its value is 2.910^-3K.  

2. Explain black body radiation.

If a body, irrespective of wavelength and angle of incidence, absorbs all the electromagnetic radiation that falls on it, it is known as a black body. The black body, to maintain equilibrium, should emit radiation that equals the amount of radiation absorbed. 

3. Give some applications of Wiens displacement law.

1. It explains the change in color of an iron rod from dull red to yellow when placed in a flame. 

2. Wiens law helps to predict the temperature on the surface of celestial bodies like the sun and moon.