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Question

Four identical rods AB,CD,CF and DE are connected as shown in figure. The length, cross- sectional area and thermal conductivity of each rod are L,A, K respectively. The ends A, E, F are maintained at temperature T subscript 1 end subscript comma text end text T subscript 2 end subscript and T subscript 3 end subscript respectively. Assuming no loss of heat to the atmosphere, calculate the temperature at B [CB = BD].

  1. fraction numerator T subscript 1 end subscript plus T subscript 2 end subscript plus T subscript 3 end subscript over denominator 3 end fraction    
  2. fraction numerator 2 text end text T subscript 1 end subscript plus 3 text end text T subscript 2 end subscript plus 5 text end text T subscript 3 end subscript over denominator 5 end fraction    
  3. fraction numerator 3 text end text T subscript 1 end subscript plus 2 text end text T subscript 2 end subscript plus 2 text end text T subscript 3 end subscript over denominator 7 end fraction    
  4. fraction numerator T subscript 1 end subscript plus 2 text end text T subscript 2 end subscript plus 3 text end text T subscript 3 end subscript over denominator 5 end fraction    

The correct answer is: fraction numerator 3 text end text T subscript 1 end subscript plus 2 text end text T subscript 2 end subscript plus 2 text end text T subscript 3 end subscript over denominator 7 end fraction

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