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Physics-

General

Easy

Question

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

75 $℃$
67 $℃$
33 $℃$
25 $℃$

The correct answer is: 75 $℃$

Let the temperature of junction be $theta.$
$open parentheses fraction numerator increment Q over denominator d subscript 1 end subscript end fraction close parentheses subscript c o p p e r end subscript blank equals open parentheses fraction numerator increment Q over denominator increment T end fraction close parentheses subscript s t e e l end subscript$
$K subscript 1 end subscript A equals blank fraction numerator open parentheses 100 minus theta close parentheses over denominator 18 end fraction equals fraction numerator K subscript 2 end subscript A open parentheses theta minus 0 close parentheses over denominator 6 end fraction$
$9 K subscript 2 end subscript fraction numerator open parentheses 100 minus theta close parentheses over denominator 3 end fraction equals K subscript 2 end subscript theta$
3 $theta equals 900 minus 9 theta$
12 $theta equals 900$
$theta equals 75 ℃$

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