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 ?

• A. 75$^\circ$C
• B. 67 $^\circ$C
• C. 25 $^\circ$C
• D. 33$^\circ$C

Answer 1

The Correct Option is A

Temperature of interface
$\theta=\frac{K_{1} \theta_{1} l_{2}+K_{2} \theta_{2} l_{1}}{K_{1} l_{2}+K_{2} l_{1}}$
It is given that $K_{ Cu }=9 K_{s} .$ So, if $K_{s}=K_{1}=K$, then
$K_{ Cu }=K_{2} =9\, K $
$\Rightarrow \,\,\,\theta =\frac{9 K \times 100 \times 6+K \times 0 \times 18}{9 K \times 6+K \times 18} $
$=\frac{5400 K }{72 K }=75^{\circ} \,C$