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Mechanical Properties Of Fluids

Question
CBSEENPH11020788

A black body at 1227°C emits radiations with maximum intensity at a wavelength of 5000 Å. If the temperature of the body is increased by 1000°C, the maximum intensity will be observed at

  • 4000 Å

  • 5000 Å

  • 6000 Å

  • 3000 Å

Solution

D.

3000 Å

The product of wavelength corresponding to maximum intensity of radiation and temperature of the body in Kelvin is constant.
According to Wien's law
   straight lambda subscript straight m straight T space equals space constant space left parenthesis say space straight b right parenthesis
where straight lambda subscript straight m is wavelength corresponding to maximum intensity of radiation and T is temperature of the body in Kelvin.
therefore space space space space straight lambda subscript straight m apostrophe end subscript over straight lambda subscript straight m space equals space fraction numerator straight T over denominator straight T apostrophe end fraction
Given,   T = 1227 + 273 = 1500 K,
             T' = 1227 + 1000 + 273 = 2500 K
              straight lambda subscript straight m space equals space 5000 space straight Å
Hence comma space space space straight lambda subscript straight m apostrophe end subscript space equals space 1500 over 2500 cross times 5000 space equals space 3000 space straight Å