(D) Since the two cylinders are arranged in parallel,the total thermal conductance is the sum of the individual thermal conductances.Thermal conductan

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(D) Since the two cylinders are arranged in parallel,the total thermal conductance is the sum of the individual thermal conductances.Thermal conductance $C = \frac{kA}{l}$.For parallel combination,$C_{eq} = C_1 + C_2$.$\frac{k_{eq} A_{total}}{l} = \frac{k_1 A_1}{l} + \frac{k_2 A_2}{l}$.Since the lengths $l$ are equal,$k_{eq} A_{total} = k_1 A_1 + k_2 A_2$.Here,$A_1 = \pi r^2$ and $A_2 = \pi ((2r)^2 - r^2) = 3\pi r^2$.The total area $A_{total} = A_1 + A_2 = 4\pi r^2$.Substituting these values: $k_{eq} (4\pi r^2) = k_1 (\pi r^2) + k_2 (3\pi r^2)$.$4 k_{eq} = k_1 + 3k_2$.$k_{eq} = \frac{1}{4} (k_1 + 3k_2)$.

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

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$A$ cylinder of thermal conductivity $k_1$ and radius $r$ is surrounded by a cylindrical shell of inner radius $r$,outer radius $2r$,and thermal conductivity $k_2$. Both cylinders have the same length and the temperature difference across their ends is the same. The equivalent thermal conductivity of the system is:

A
$1/3 (k_1 + 2k_2)$
B
$1/2 (2k_1 + 3k_2)$
C
$1/4 (3k_1 + k_2)$
D
$1/4 (k_1 + 3k_2)$

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10-2.Heat Transfer

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Thermal Resistance and it's Combination

$A$ copper rod $2 \ m$ long has a circular cross-section of radius $1 \ cm$. One end is kept at $100^{\circ}C$ and the other at $0^{\circ}C$,and the surface is covered by non-conducting material to prevent heat losses through the surface. The thermal resistance of the bar in Kelvin per Watt is (Take thermal conductivity $K = 401 \ W/m-K$ of copper):- (in $.9$)

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Five wires each of cross-sectional area $A$ and length $l$ are combined as shown. The thermal conductivity of copper and steel are $k_1$ and $k_2$ respectively. The equivalent thermal resistance between $A$ and $C$ is

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Two identical square metal rods are welded end-to-end as shown in figure $(a)$. $20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If they are joined as shown in figure $(b)$,the same amount of heat will flow in ...... minutes.

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Two rods having thermal conductivity in the ratio of $5:3$,having equal lengths and equal cross-sectional area,are joined face to face. If the temperature of the free end of the first rod is $100^{\circ}C$ and the free end of the second rod is $20^{\circ}C$,then the temperature of the junction is...... $^{\circ}C$.

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Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in the figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ}C$ and $40^{\circ}C$ respectively. Given the thermal conductivity of rod $x$ is three times that of rod $y$, the temperatures at junction points $B$ and $E$ are (close to):

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Five wires each of cross-sectional area $A$ and length $l$ are combined as shown. The thermal conductivity of copper and steel are $k_1$ and $k_2$ respectively. The equivalent thermal resistance between $A$ and $C$ is

Two identical square metal rods are welded end-to-end as shown in figure $(a)$. $20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If they are joined as shown in figure $(b)$,the same amount of heat will flow in ...... minutes.

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