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Question

A composite metal bar of uniform section is made up of length 25 cm of copper, 10 cm of nickel and 15 cm of aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at 10 0 to the power of o end exponent C and the aluminium end at 0 to the power of o end exponent C. The whole rod is covered with belt so that there is no heat loss occurs at the sides. If K subscript text Cu end text end subscript equals 2 K subscript A l end subscript and K subscript A l end subscript equals 3 K subscript text Ni end text end subscript, then what will be the temperatures of C u minus N i and N i minus A l junctions respectively

  1. 23.3 3 to the power of o end exponent C and A    
  2. 83.3 3 to the power of o end exponent C and 2 0 to the power of o end exponent C    
  3. 5 0 to the power of o end exponent C and 3 0 to the power of o end exponent C    
  4. 3 0 to the power of o end exponent C and 5 0 to the power of o end exponent C    

The correct answer is: 83.3 3 to the power of o end exponent C and 2 0 to the power of o end exponent C


    If suppose K subscript N i end subscript equals K rightwards double arrow K subscript A l end subscript equals 3 K and K subscript C u end subscript equals 6 K.
    Since all metal bars are connected in series
    So open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C u end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A l end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript N i end subscript
    and fraction numerator 3 over denominator K subscript e q end subscript end fraction equals fraction numerator 1 over denominator K subscript C u end subscript end fraction plus fraction numerator 1 over denominator K subscript A l end subscript end fraction plus fraction numerator 1 over denominator K subscript N i end subscript end fraction equals fraction numerator 1 over denominator 6 K end fraction plus fraction numerator 1 over denominator 3 K end fraction plus fraction numerator 1 over denominator K end fraction equals fraction numerator 9 over denominator 6 K end fraction
    Þ K subscript e q end subscript equals 2 K

    Hence, if open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C u end subscript
    Þ fraction numerator K subscript e q end subscript A left parenthesis 100 minus 0 right parenthesis over denominator l subscript C o m b i n a t i o n end subscript end fraction equals fraction numerator K subscript C u end subscript A left parenthesis 100 minus theta subscript 1 end subscript right parenthesis over denominator l subscript C u end subscript end fraction
    Þ fraction numerator 2 K A left parenthesis 100 minus 0 right parenthesis over denominator left parenthesis 25 plus 10 plus 1 left parenthesis e right parenthesis blank end fraction equals fraction numerator 6 K A left parenthesis 100 minus theta subscript 1 end subscript right parenthesis over denominator 25 end fraction Þ theta subscript 1 end subscript equals 83.33 degree C
    Similar if open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A l end subscript
    Þ fraction numerator 2 K A left parenthesis 100 minus 0 right parenthesis over denominator 50 end fraction equals fraction numerator 3 K A left parenthesis theta subscript 2 end subscript minus 0 right parenthesis over denominator 15 end fractionÞ theta subscript 2 end subscript equals 2 0 to the power of o end exponent C

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