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

Answer: (A)

Temperature of the 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 $K_{Cu}=9K_s$ . So, if $K_s=K_1=K$ , then
$K_{Cu}=K_2=9K$
$\Rightarrow$ $\theta =\frac{9K\times 100\times 6+K\times 0\times 18}{9K\times 6+K\times 18}$
$=\frac{5400K}{72K}=75^{\circ }C$