(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 10-2.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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Three rods of the same dimensions have thermal conductivities $3K, 2K$, and $K$. They are arranged as shown in the figure. The temperature of the junction in the steady state is:

In the Ingen-Hauz's experiment,the wax melts up to lengths $10 \ cm$ and $25 \ cm$ on two identical rods of different materials. The ratio of thermal conductivities of the two materials is:

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For a spherical shell with inner and outer radii $r_1$ and $r_2$ respectively,the formula for the heat flow rate is = ......... where $T_1$ and $T_2$ are the temperatures of the inner and outer surfaces of the shell $(T_1 > T_2)$. The thermal conductivity of the material of the shell is $k$.

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