Wien's Displacement Law

 Wien's Displacement Law

Introduction: From the black body spectrum, it is clear that as the temperature goes on increasing, the wavelength corresponding to maximum emissive power goes on decreasing. The graph of wavelength and emissive power shifts toward left. Thus the above conclusion result in formation of very important result which was explained using wien's displacement law.

Statement: 

The wavelength for which emissive  power of a  blackbody is maximum is inversely proportional to the absolute temperature of the black  body.

Mathematically, 

λ_max  ∝  1/T

λ_max  = b  x  1 / T 

where b is called as wien's constant. 

b= 2.898 x 10^-3 mK.

This law is  also referred to as displacement law as the temperature increases the , the maximum intensity of radiation emitted by body gets shifted towards shorter wavelength.

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Emissive Power and Absorptive Power

Emissive power of  a body at a given  temperature is defined as the amount of heat radiation emitted by the body per unit surface area per unit time at the same temperature. 

Mathematically,

R = Q /At

R = Emissive power of a body 

Q = radiant energy emitted 

A surface area of the body

t= Time for which body radiated energy

It's SI unit is J/m² s

Dimension [ L⁰   M¹   T^-3] 

Note: Every body radiated heat radiation at all temperature except absolute zero.

At  a given temperature black body has maximum emissive power hence, it is convenient to compare emissive power of a body with emissive power of perfectly black body at same temperature.

Coefficient of emission or emissivity  : Coefficicent of emission of a body is the ratio of emissive power of a body at aa given temperature to the emissive power of a perfectly black body. at the same temperature.

Mathematically,

e = R /R_b

e = coefficient of emission

R= Emissive power of a body

R_b = Emissive power of perfectly black body.

 For perfectly black body , e= 1

 For ordinary bodies , e < 1

<<<Radiation Spectrum>>> │<<<Kirchoff's Law of heat>>>

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