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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

$50 ℃$
$\frac{100}{3} ℃$
$60 ℃$
$\frac{200}{3} ℃$

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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