(A) The rate of heat flow through a rod is given by the formula: $\frac{dQ}{dt} = \frac{KA(\Delta \theta)}{l}$Given that the rate of heat flow $\frac{

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(A) The rate of heat flow through a rod is given by the formula: $\frac{dQ}{dt} = \frac{KA(\Delta \theta)}{l}$Given that the rate of heat flow $\frac{dQ}{dt}$ and the cross-sectional area $A$ are the same for both rods,we can write:$\frac{K_A \Delta \theta_A}{l_A} = \frac{K_B \Delta \theta_B}{l_B}$Substituting the given values:$l_A = 40\, cm$,$\Delta \theta_A = 80^\circ C$$l_B = 60\, cm$,$\Delta \theta_B = 90^\circ C$$\frac{K_A \times 80}{40} = \frac{K_B \times 90}{60}$$2 K_A = 1.5 K_B$$\frac{K_A}{K_B} = \frac{1.5}{2} = \frac{3}{4}$Therefore,the ratio of their thermal conductivities is $3:4$.

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

Medium

$A$ rod $A$ of length $40\, cm$ has a temperature difference of $80^\circ C$ at its two ends. Another rod $B$ of length $60\, cm$ has a temperature difference of $90^\circ C$ at its ends. Both rods have the same area of cross-section. If the rate of flow of heat is the same for both,then the ratio of their thermal conductivities $(K_A : K_B)$ will be:

A
$3:4$
B
$4:3$
C
$1:2$
D
$2:1$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

The temperature difference across two cylindrical rods $A$ and $B$ of the same material and same mass are $40^{\circ} C$ and $60^{\circ} C$ respectively. In steady state,if the rates of flow of heat through the rods $A$ and $B$ are in the ratio $3: 8$,the ratio of the lengths of the rods $A$ and $B$ is (in $: 3$)

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Four rods with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperatures. Which one will conduct the most heat?

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How is thermal conduction represented for a given temperature difference for any material by the rate of heat conduction?

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Two identical long bars $A$ and $B$ made of different materials are coated with wax and have one end immersed in a hot oil bath. When the steady state is reached,the lengths for which the wax melts are $l_A$ and $l_B$. If $k_A$ and $k_B$ are the thermal conductivities of the materials,then:

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Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,then the ratio of the amounts of heat conducted through per unit time will be

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