(B) The rate of heat flow through a rod is given by: $\dot{Q} = \frac{KA \Delta T}{l}$.Since the rods are connected in series,the rate of heat flow $\

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$\frac{T_A}{T_B} = \frac{1}{3}$

(B) The rate of heat flow through a rod is given by: $\dot{Q} = \frac{KA \Delta T}{l}$.Since the rods are connected in series,the rate of heat flow $\dot{Q}$ through both rods must be the same.For rod $A$ (thermal conductivity $3K$): $\dot{Q}_A = \frac{(3K)A T_A}{l}$.For rod $B$ (thermal conductivity $K$): $\dot{Q}_B = \frac{KA T_B}{l}$.Since $\dot{Q}_A = \dot{Q}_B$,we have:$\frac{3KA T_A}{l} = \frac{KA T_B}{l}$$3 T_A = T_B$Therefore,$\frac{T_A}{T_B} = \frac{1}{3}$.

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

Difficult

Two rods $A$ and $B$ of the same cross-sectional area $A$ and length $l$ are connected in series between a source $(T_1 = 100^{\circ}C)$ and a sink $(T_2 = 0^{\circ}C)$ as shown in the figure. The rods are laterally insulated. If the thermal conductivities of rods $A$ and $B$ are $3K$ and $K$ respectively,and $T_A$ and $T_B$ are the temperature drops across rods $A$ and $B$,then:

A
$\frac{T_A}{T_B} = \frac{3}{1}$
B
$\frac{T_A}{T_B} = \frac{1}{3}$
C
$\frac{T_A}{T_B} = \frac{3}{4}$
D
$\frac{T_A}{T_B} = \frac{4}{3}$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

Rate of flow of heat through a cylindrical rod is $H_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same, and if the rate of flow of heat becomes $H_2$, then $H_2 =$

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When is thermal conductivity said to be constant?

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The thermal conductivity of a wire is $1.7 \ W \ m^{-1} \ K^{-1}$ and that of cement is $2.9 \ W \ m^{-1} \ K^{-1}$. The thickness of the cement insulation is $..... \ cm$. Here,the thickness of the wire is $20 \ cm$.

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$A$ rod of length $L$ with sides fully insulated is made of a material whose thermal conductivity varies with temperature $T$ as $K = \frac{\alpha}{T}$,where $\alpha$ is a constant. The ends of the rod are kept at temperatures $T_1$ and $T_2$. The temperature $T$ at a distance $x$ from the end kept at $T_1$ is:

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Two plates of the same area are placed in contact. Their thicknesses as well as their thermal conductivities are in the ratio $2:3$. The outer surface of one plate is maintained at $10^{\circ} C$ and that of the other at $0^{\circ} C$. The temperature at the common surface is (in $^{\circ} C$)

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Rate of flow of heat through a cylindrical rod is $H_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same, and if the rate of flow of heat becomes $H_2$, then $H_2 =$

When is thermal conductivity said to be constant?

The thermal conductivity of a wire is $1.7 \ W \ m^{-1} \ K^{-1}$ and that of cement is $2.9 \ W \ m^{-1} \ K^{-1}$. The thickness of the cement insulation is $..... \ cm$. Here,the thickness of the wire is $20 \ cm$.

Two plates of the same area are placed in contact. Their thicknesses as well as their thermal conductivities are in the ratio $2:3$. The outer surface of one plate is maintained at $10^{\circ} C$ and that of the other at $0^{\circ} C$. The temperature at the common surface is (in $^{\circ} C$)

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