(D) In a steady state,the rate of heat flow through both rods must be equal.Let $\theta$ be the temperature at the junction.The rate of heat flow is g

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(D) In a steady state,the rate of heat flow through both rods must be equal.Let $\theta$ be the temperature at the junction.The rate of heat flow is given by $H = \frac{KA(T_1 - T_2)}{\ell}$.Since the rods are in series,the heat current $H$ is the same for both.$H_{Cu} = H_{Steel}$$\frac{K_{Cu} A (100 - \theta)}{\ell} = \frac{K_{Steel} A (\theta - 0)}{\ell}$Given $K_{Cu} = 385 \, W \, m^{-1} \, K^{-1}$ and $K_{Steel} = 50 \, W \, m^{-1} \, K^{-1}$.$385(100 - \theta) = 50(\theta - 0)$Divide by $5$:$77(100 - \theta) = 10\theta$$7700 - 77\theta = 10\theta$$87\theta = 7700$$\theta = \frac{7700}{87} \approx 88.5^{\circ} \, C$.

Class 11 Physics 2 Thermal Properties of Matter: Heat Transfer Heat Conduction and Thermal Conductivity

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Two rods,one made of copper and the other made of steel,of the same length and same cross-sectional area,are joined together. The thermal conductivities of copper and steel are $385 \, W \, m^{-1} \, K^{-1}$ and $50 \, W \, m^{-1} \, K^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ} \, C$ and $0^{\circ} \, C$ respectively. The temperature at the junction is nearly $.......^{\circ} \, C$.

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$12$
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$73$
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$88.5$

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2 Thermal Properties of Matter: Heat Transfer

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Heat Conduction and Thermal Conductivity

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Three conducting rods of the same material and cross-section are shown in the figure. The temperatures of $A$,$D$,and $C$ are maintained at $20^{\circ} C$,$90^{\circ} C$,and $0^{\circ} C$ respectively. If there is no heat flow in rod $AB$,the ratio of the lengths of $BD$ and $BC$ is:

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