(C) In a steady state,the rate of heat flow through both rods must be equal.Let $A$ be the cross-sectional area,$L_1 = 1 \ cm$,$L_2 = 2 \ cm$,$K_1 = K

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(C) In a steady state,the rate of heat flow through both rods must be equal.Let $A$ be the cross-sectional area,$L_1 = 1 \ cm$,$L_2 = 2 \ cm$,$K_1 = K$,$K_2 = 3K$,$T_1 = 0^{\circ}C$,$T_2 = 100^{\circ}C$,and $\phi$ be the interface temperature.The rate of heat flow is given by $H = \frac{KA(T_{high} - T_{low})}{L}$.For the first rod: $H_1 = \frac{K \cdot A \cdot (\phi - 0)}{1}$.For the second rod: $H_2 = \frac{3K \cdot A \cdot (100 - \phi)}{2}$.Since $H_1 = H_2$,we have:$K \cdot A \cdot \phi = \frac{3K \cdot A \cdot (100 - \phi)}{2}$$\phi = \frac{3(100 - \phi)}{2}$$2\phi = 300 - 3\phi$$5\phi = 300$$\phi = 60^{\circ}C$.

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

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Two rods with thermal conductivities $K$ and $3K$ and equal cross-sectional areas are joined as shown in the figure. Their lengths are $1 \ cm$ and $2 \ cm$,respectively. If the temperatures of the two ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ (see figure),then the temperature $\phi$ of their interface is:

A
$50^{\circ}C$
B
$\frac{100}{3}^{\circ}C$
C
$60^{\circ}C$
D
$\frac{200}{3}^{\circ}C$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

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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The ends of two rods of different materials with their thermal conductivities,radii of cross-sections,and lengths all in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4 \; cal/sec$,the rate of flow of heat in the shorter rod in $cal/sec$ will be:

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$A$ 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:

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One end of a metal rod of length $1.0 \ m$ and area of cross-section $100 \ cm^2$ is maintained at $100^{\circ}C$. If the other end of the rod is maintained at $0^{\circ}C$,the quantity of heat transmitted through the rod per minute is (Coefficient of thermal conductivity of the material of the rod = $100 \ W/m-K$).

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Which of the following circular rods (given radius $r$ and length $l$),each made of the same material and whose ends are maintained at the same temperature difference,will conduct the most heat?

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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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