Physics-
General
Easy

Question

The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?

  1. 75℃    
  2. 67℃    
  3. 25℃    
  4. 33℃    

The correct answer is: 75℃


    Temperature of interface
    theta equals fraction numerator K subscript 1 end subscript theta subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript theta subscript 2 end subscript l subscript 1 end subscript over denominator K subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript l subscript 1 end subscript end fraction
    It is given that K subscript C u end subscript equals 9 K subscript s end subscript. So, if K subscript s end subscript equals K subscript 1 end subscript equals K, then
    K subscript C u end subscript equals K subscript 2 end subscript equals 9 K
    rightwards double arrow theta equals fraction numerator 9 K cross times 100 cross times 6 plus K cross times 0 cross times 18 over denominator 9 K cross times 6 plus K cross times 18 end fraction
    equals fraction numerator 5400 K over denominator 72 K end fraction equals 75 ℃

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