Physics-
General
Easy

Question

Two bars of thermal conductivities K and 3 K and lengths 1 c m and 2 c m respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is 0 ℃ and 100 ℃ respectively (see figure), then the temperature ϕ of the interface is

  1. 50 ℃    
  2. fraction numerator 100 over denominator 3 end fraction ℃    
  3. 60 ℃    
  4. fraction numerator 200 over denominator 3 end fraction ℃    

The correct answer is: 60 ℃


    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 equals fraction numerator K cross times 0 cross times 2 plus 3 K cross times 100 cross times 1 over denominator K cross times 2 plus 3 K cross times 1 end fraction
    equals fraction numerator 300 K over denominator 5 K end fraction equals 60 ℃

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