(A) When two rods are connected in series, the total thermal resistance $R_{eq}$ is the sum of individual thermal resistances $R_1$ and $R_2$.The ther

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$\frac{(l_1+l_2) k_1 k_2}{k_2 l_1+k_1 l_2}$

(A) When two rods are connected in series, the total thermal resistance $R_{eq}$ is the sum of individual thermal resistances $R_1$ and $R_2$.The thermal resistance of a rod is given by $R = \frac{l}{kA}$.For the two rods in series: $R_{eq} = R_1 + R_2$.$\frac{l_1+l_2}{k A} = \frac{l_1}{k_1 A} + \frac{l_2}{k_2 A}$.Canceling the area $A$ from both sides:$\frac{l_1+l_2}{k} = \frac{l_1}{k_1} + \frac{l_2}{k_2}$.$\frac{l_1+l_2}{k} = \frac{k_2 l_1 + k_1 l_2}{k_1 k_2}$.Therefore, $k = \frac{(l_1+l_2) k_1 k_2}{k_2 l_1 + k_1 l_2}$.

Class 11 Physics 10-2.Heat Transfer Thermal Resistance and it's Combination

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Two rods whose lengths are $l_1$ and $l_2$ with thermal conductivity coefficients $k_1$ and $k_2$ are placed end to end. The thermal conductivity coefficient of a uniform rod of length $l_1+l_2$ whose thermal resistance is the same as that of the system of these two rods is

TS EAMCET 2021 All TS EAMCET

A
$\frac{(l_1+l_2) k_1 k_2}{k_2 l_1+k_1 l_2}$
B
$\frac{(l_1+l_2) k_1 k_2}{k_1 l_1+k_2 l_2}$
C
$\frac{k_1 l_1+k_2 l_2}{(l_1+l_2) k_1 k_2}$
D
$\frac{k_1 l_2+k_2 l_1}{(l_1+l_2) k_1 k_2}$

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10-2.Heat Transfer

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Thermal Resistance and it's Combination

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In the following figure,two insulating sheets with thermal resistances $R$ and $3R$ are shown. The temperature $\theta$ at the interface is ...... $^oC$.

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Two rods whose lengths are $l_1$ and $l_2$ with thermal conductivity coefficients $k_1$ and $k_2$ are placed end to end. The thermal conductivity coefficient of a uniform rod of length $l_1+l_2$ whose thermal resistance is the same as that of the system of these two rods is

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The rate of flow of heat through a metal rod with a temperature difference of $40^{\circ} C$ is $1600 cal/s$. The thermal resistance of the metal rod in $^{\circ} C s/cal$ is

In the following figure,two insulating sheets with thermal resistances $R$ and $3R$ are shown. The temperature $\theta$ at the interface is ...... $^oC$.

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures of $200^oC$ and $20^oC$ respectively. The temperature of junction $B$ will be ....... $^oC$.

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