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Question

The adjoining diagram shows the spectral energy density distribution E subscript lambda end subscript of 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. 32000 blank K    
  2. 16000 blank K    
  3. 8000 blank K    
  4. 4000 blank K    

The correct answer is: 4000 blank 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
    rightwards double arrow fraction numerator A subscript T end subscript 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 exponent rightwards double arrow 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 exponent rightwards double arrow T equals 4000 K

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