(C) In a steady state,the rate of heat flow through both bars must be equal.Let the interface temperature be $\varphi$.The rate of heat flow $H$ is gi

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(C) In a steady state,the rate of heat flow through both bars must be equal.Let the interface temperature be $\varphi$.The rate of heat flow $H$ is given by $H = \frac{KA(\Delta T)}{L}$.For the first bar: $H_1 = \frac{K \cdot A \cdot (\varphi - 0)}{1}$.For the second bar: $H_2 = \frac{3K \cdot A \cdot (100 - \varphi)}{2}$.Since $H_1 = H_2$,we have:$K \cdot A \cdot \varphi = \frac{3K \cdot A \cdot (100 - \varphi)}{2}$.Canceling $K$ and $A$ from both sides:$\varphi = \frac{3(100 - \varphi)}{2}$.$2\varphi = 300 - 3\varphi$.$5\varphi = 300$.$\varphi = 60\,^{\circ}C$.

Class 11 Physics 10-2.Heat Transfer Heat Conduction and Thermal Conductivity

Medium

Two bars of thermal conductivities $K$ and $3K$ and lengths $1\, cm$ and $2\, cm$ respectively have equal cross-sectional area. They are joined length-wise as shown in the figure. If the temperatures at the ends of this composite bar are $0\,^{\circ}C$ and $100\,^{\circ}C$ respectively,then the temperature $\varphi$ of the interface is......... $^oC$.

A
$50$
B
$\frac{100}{3}$
C
$60$
D
$\frac{200}{3}$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

If $6000 \ J/s$ of heat flows through a conductor of length $1 \ m$ and cross-sectional area $0.75 \ m^2$,then the temperature difference between its ends is ...... $^\circ C$. $[K = 200 \ J/(m \cdot K)]$

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Two sheets of thickness $d$ and $3d$ are touching each other. The temperature just outside the thinner sheet side is $A$,and on the side of the thicker sheet is $C$. The interface temperature is $B$. If $A, B$,and $C$ are in arithmetic progression,the ratio of the thermal conductivity of the thinner sheet to the thicker sheet is:

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When is thermal conductivity said to be constant?

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Two rods of same length and cross-section are joined along their length. The thermal conductivities of the first and second rods are $K_1$ and $K_2$,respectively. The temperatures of the free ends of the first and second rods are maintained at $\theta_1$ and $\theta_2$,respectively. The temperature of the common junction is:

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$A$ heat source at $T_1 = 10^3\, K$ is connected to another heat reservoir at $T_2 = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, W\, K^{-1}\, m^{-1}$,the energy flux through it in the steady state is ........... $W\, m^{-2}$.

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If $6000 \ J/s$ of heat flows through a conductor of length $1 \ m$ and cross-sectional area $0.75 \ m^2$,then the temperature difference between its ends is ...... $^\circ C$. $[K = 200 \ J/(m \cdot K)]$

When is thermal conductivity said to be constant?

$A$ heat source at $T_1 = 10^3\, K$ is connected to another heat reservoir at $T_2 = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, W\, K^{-1}\, m^{-1}$,the energy flux through it in the steady state is ........... $W\, m^{-2}$.

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