Abstract
The oscillators of a perfect blackbody are considered as non-interacting entities. Thus, Bose-Einstein Condensation is possible for these entities. The Bose-Einstein Condensate (BEC) temperature of a perfect blackbody is calculated from the Planck’s theory of blackbody radiation and de Broggle’s wave-particle duality relation. It is observed that the BEC temperature of an ideal blackbody is 4.0K. Thus, bellow 4.0K temperature the energy density vs wavelength plot of a blackbody would look like a delta function. In this region, a blackbody would absorb or emit radiation of unique frequency depending upon its temperature. It is also possible to calculate the rest mass and the ground state vibrational energy of the oscillators of a blackbody using present formalism.
Highlights
Bose-Einstein condensation (BEC) was predicted in 1924.1–4 But, it took nearly seventy years to obtain such state through experiment.[5]
BEC is achieved for different systems and its properties are well studied
It is possible to obtain a state of unique features similar to BEC for the oscillators of a blackbody which are considered as non-interacting entities
Summary
Bose-Einstein condensation (BEC) was predicted in 1924.1–4 But, it took nearly seventy years to obtain such state through experiment.[5]. BEC requires cooling of a sample so that its thermal de Brogglie wavelength, λdb, becomes larger than the mean spacing between two particles of the system Exploiting this condition it is possible to calculate the condensation temperature of a blackbody. Zero entropy of a system at a finite temperature is possible This temperature is the critical temperature of the system for Bose-Einstein Condensation. From the gas law of thermodynamics, we could not derive any relation to find out the critical temperature of a material at which its entropy is zero. We use the wave-particle duality relation and Planck’s theory of blackbody radiation to find out the critical temperature of a perfect blackbody at which its thermal entropy becomes zero. The mass of the resonator of a perfect blackbody is calculated which is very close to the value of the mass of a resonator reported earlier
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