(A) In steady state,the rate of heat flow through both sections is the same.Let $T$ be the temperature at the interface.The rate of heat flow $H$ is g

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$\frac{K_1 l_2 T_1 + K_2 l_1 T_2}{K_1 l_2 + K_2 l_1}$

(A) In steady state,the rate of heat flow through both sections is the same.Let $T$ be the temperature at the interface.The rate of heat flow $H$ is given by $H = \frac{KA(T_{high} - T_{low})}{l}$.For the first section: $H = \frac{K_1 A(T_1 - T)}{l_1}$.For the second section: $H = \frac{K_2 A(T - T_2)}{l_2}$.Equating the two rates: $\frac{K_1 A(T_1 - T)}{l_1} = \frac{K_2 A(T - T_2)}{l_2}$.$\frac{K_1(T_1 - T)}{l_1} = \frac{K_2(T - T_2)}{l_2}$.$K_1 l_2(T_1 - T) = K_2 l_1(T - T_2)$.$K_1 l_2 T_1 - K_1 l_2 T = K_2 l_1 T - K_2 l_1 T_2$.$K_1 l_2 T_1 + K_2 l_1 T_2 = T(K_1 l_2 + K_2 l_1)$.$T = \frac{K_1 l_2 T_1 + K_2 l_1 T_2}{K_1 l_2 + K_2 l_1}$.

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

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One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is

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A
$\frac{K_1 l_2 T_1 + K_2 l_1 T_2}{K_1 l_2 + K_2 l_1}$
B
$\frac{K_2 l_1 T_1 + K_1 l_2 T_2}{K_2 l_1 + K_1 l_2}$
C
$\frac{K_1 l_1 T_1 + K_2 l_2 T_2}{K_1 l_1 + K_2 l_2}$
D
$\frac{K_2 l_2 T_1 + K_1 l_1 T_2}{K_1 l_1 + K_2 l_2}$

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2 Thermal Properties of Matter: Heat Transfer

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Heat Conduction and Thermal Conductivity

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Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$,respectively. If the rate of heat conduction in rod $1$ is four times that in rod $2$,then:

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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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The thickness of a metallic plate is $0.4 \ cm$. The temperature difference between its two surfaces is $20^{\circ}C$. The quantity of heat flowing per second is $50 \ \text{calories}$ through an area of $5 \ cm^2$. In the $CGS$ system,the coefficient of thermal conductivity is:

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The thickness of a uniform rectangular metal plate is $5 \ mm$ and the area of each surface is $5 \ cm^2$. In steady state, the temperature difference between the two surfaces of the plate is $14^{\circ} C$. If the heat flowing through the plate in one second from one surface to the other surface is $42 \ J$, then the thermal conductivity of the metal 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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One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is

Similar Questions

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$,respectively. If the rate of heat conduction in rod $1$ is four times that in rod $2$,then:

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 $^oC$).

The thickness of a metallic plate is $0.4 \ cm$. The temperature difference between its two surfaces is $20^{\circ}C$. The quantity of heat flowing per second is $50 \ \text{calories}$ through an area of $5 \ cm^2$. In the $CGS$ system,the coefficient of thermal conductivity is:

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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