Physics-
General
Easy

Question

The adjoining diagram shows the spectral energy density distribution E subscript lambda end subscriptof a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is

  1. 32,000 K    
  2. 16,000 K    
  3. 8,000 K    
  4. 4,000 K    

The correct answer is: 4,000 K


    fraction numerator A subscript T end subscript over denominator A subscript 2000 end subscript end fraction equals fraction numerator 16 over denominator 1 end fraction (given)
    Area under e subscript lambda end subscript minus lambda curve represents the emissive power of body and emissive power proportional to T to the power of 4 end exponent
    (Hence area under e subscript lambda end subscript minus lambda curve) proportional to T to the power of 4 end exponent
    Þfraction numerator A T over denominator A subscript 2000 end subscript end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponentÞ fraction numerator 16 over denominator 1 end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponentÞ T equals 4000 K.

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