The thermal conductivity of copper is 9 times | vedclass

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(C) Let the thermal conductivity of steel be $K_s = K$. Then the thermal conductivity of copper is $K_{cu} = 9K$.Let the length of the copper rod be $

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$33$

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(C) Let the thermal conductivity of steel be $K_s = K$. Then the thermal conductivity of copper is $K_{cu} = 9K$.Let the length of the copper rod be $L_{cu} = 18 \ cm$ and the length of the steel rod be $L_s = 6 \ cm$.The temperatures at the ends are $T_1 = 100 \ ^oC$ and $T_2 = 0 \ ^oC$.In steady state,the rate of heat flow through both rods is the same:$\frac{K_{cu} A (T_1 - T)}{L_{cu}} = \frac{K_s A (T - T_2)}{L_s}$Where $T$ is the junction temperature and $A$ is the cross-sectional area.Substituting the values:$\frac{9K (100 - T)}{18} = \frac{K (T - 0)}{6}$$\frac{100 - T}{2} = T$$100 - T = 2T$$3T = 100$$T = \frac{100}{3} \approx 33.33 \ ^oC$.

The thermal conductivity of copper is $9$ times that of steel. Find the temperature of the junction of copper and steel in the composite rod as shown in the figure (in $^oC$).

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