(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

Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$,respectively,are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $\theta_2$ and $\theta_1$ respectively $(\theta_2 > \theta_1)$. The temperature at the interface is

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Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

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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 $G_A$ and $G_B$ are the temperature gradients across rod $A$ (thermal conductivity $3K$) and rod $B$ (thermal conductivity $K$),then:

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On which factor does the thermal conductivity depend?

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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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Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

On which factor does the thermal conductivity depend?

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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