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Question

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be

  1. 45°C
  2. 60°C
  3. 30°C
  4. 20°C

The correct answer is: 60°C


    Let the temperature of junction  be θ. Since roads Band C are parallel to each other (because both having the same temperature difference). Hence given figure can be redrawn as follows


    because space of 1em Q over t equals fraction numerator open parentheses theta subscript 1 minus theta subscript 2 close parentheses over denominator R end fraction text  and  end text open parentheses Q over t close parentheses subscript A B end subscript equals open parentheses Q over t close parentheses subscript B C end subscript
not stretchy rightwards double arrow space of 1em fraction numerator left parenthesis 90 minus theta right parenthesis over denominator R divided by 2 end fraction equals fraction numerator left parenthesis theta minus 0 right parenthesis over denominator R end fraction not stretchy rightwards double arrow 180 minus 2 theta equals theta not stretchy rightwards double arrow theta equals 60 to the power of ring operator straight C

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