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 the copper and steel.

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$33^{o} C$

$67^{o} C$

$25^{o} C$

$75^{o} C$

answer is A.

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Detailed Solution

Rate of heat flow far both the rods are same.
$\frac{Q}{t} = KA (\frac{θ_{1} - θ_{2}}{l}) = constant$
$\Rightarrow \frac{9 KA (100 ° - θ)}{18} = \frac{KA (θ - 0 °)}{6}$
$\Rightarrow 300 ° - 3 θ = θ$
$\Rightarrow θ = 75^{o} C$

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