The coefficient of thermal conductivity of copper is nine 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 ....... $^oC$
Medium
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(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 ${K_{Cu}} = {K_2} = 9K$
==> $\theta = \frac{{9K \times 100 \times 6 + K \times 0 \times 18}}{{9K \times 6 + K \times 18}}$=$\frac{{5400K}}{{72K}} = 75^\circ C$
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