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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?

75 $℃$
67 $℃$
25 $℃$
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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