(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

Two thin metallic spherical shells of radii $r_{1}$ and $r_{2}$ $(r_{1} < r_{2})$ are placed with their centres coinciding. $A$ material of thermal conductivity $K$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}$ $(\theta_{1} < \theta_{2})$. The rate at which heat flows radially through the material is:

DifficultJEE MAIN 2021

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Two plates of equal area are placed in series. The ratios of their thicknesses and thermal conductivities are both $2:3$. The temperature of the outer surface of one plate is $100 ^\circ C$ and that of the other is $0 ^\circ C$. The temperature of the common surface is ....... $^\circ C$.

Medium

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Consider two rods of same length and different specific heats $(S_{1}, S_{2})$,conductivities $(K_{1}, K_{2})$ and area of cross-sections $(A_{1}, A_{2})$ and both having temperatures $T_{1}$ and $T_{2}$ at their ends. If the rate of loss of heat due to conduction is equal,then:

MediumAIPMT 2002

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The temperature drop through each layer of a two-layer furnace wall is shown in the figure. Assume that the external temperatures $T_1$ and $T_3$ are maintained constant and $T_1 > T_3$. If the thicknesses of the layers $x_1$ and $x_2$ are the same,which of the following statements is correct?

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$A$ metal rod of length $10 \text{ cm}$ and area of cross-section $2.8 \times 10^{-4} \text{ m}^2$ is covered with a non-conducting substance. One end of it is maintained at $80^{\circ} \text{C}$,while the other end is put in ice at $0^{\circ} \text{C}$. It is found that $20 \text{ g}$ of ice melts in $5 \text{ min}$. The thermal conductivity of the metal in $\text{J s}^{-1} \text{ m}^{-1} \text{ K}^{-1}$ is (Latent heat of ice is $80 \text{ cal g}^{-1}$.)

DifficultAP EAMCET 2019

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Two plates of equal area are placed in series. The ratios of their thicknesses and thermal conductivities are both $2:3$. The temperature of the outer surface of one plate is $100 ^\circ C$ and that of the other is $0 ^\circ C$. The temperature of the common surface is ....... $^\circ C$.

Consider two rods of same length and different specific heats $(S_{1}, S_{2})$,conductivities $(K_{1}, K_{2})$ and area of cross-sections $(A_{1}, A_{2})$ and both having temperatures $T_{1}$ and $T_{2}$ at their ends. If the rate of loss of heat due to conduction is equal,then:

The temperature drop through each layer of a two-layer furnace wall is shown in the figure. Assume that the external temperatures $T_1$ and $T_3$ are maintained constant and $T_1 > T_3$. If the thicknesses of the layers $x_1$ and $x_2$ are the same,which of the following statements is correct?

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