(D) In the steady state,the rate of heat flow through cube $A$ must be equal to the rate of heat flow through cube $B$.Let $K_A = 300 \, W/m \, ^\circ

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(D) In the steady state,the rate of heat flow through cube $A$ must be equal to the rate of heat flow through cube $B$.Let $K_A = 300 \, W/m \, ^\circ C$,$K_B = 200 \, W/m \, ^\circ C$,$L_A = L_B = L$,and $A_A = A_B = A$.The rate of heat flow is given by $H = \frac{KA(T_1 - T_2)}{L}$.Equating the heat flow rates: $\frac{K_A A (100 - t)}{L} = \frac{K_B A (t - 0)}{L}$.$300(100 - t) = 200(t)$.$3(100 - t) = 2t$.$300 - 3t = 2t$.$5t = 300$.$t = 60 \, ^\circ C$.

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

Difficult

Two metal cubes $A$ and $B$ of the same size are arranged as shown in the figure. The ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. If the thermal conductivities of $A$ and $B$ are $300 \, W/m \, ^\circ C$ and $200 \, W/m \, ^\circ C$ respectively,find the temperature $t$ at the junction when the steady state is reached.

A
$45$
B
$90$
C
$30$
D
$60$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

Three rods of the same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown in the figure with their ends at $100\,^{\circ}C, 50\,^{\circ}C$ and $20\,^{\circ}C$. The temperature of their junction is....... $^{\circ}C$

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Four identical conducting rods are joined to form a square $ABCD$. The temperatures of junctions $A, B,$ and $C$ are maintained at $100^{\circ}C, 40^{\circ}C,$ and $0^{\circ}C$ respectively. Choose the $\text{INCORRECT}$ statement for this arrangement in a steady state. (The value of $\frac{KA}{L} = 1 \text{ J}/(s \cdot ^{\circ}C)$).

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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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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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Two bars of thermal conductivities $K$ and $3K$ and lengths $1\, cm$ and $2\, cm$ respectively have equal cross-sectional area. They are joined length-wise as shown in the figure. If the temperatures at the ends of this composite bar are $0\,^{\circ}C$ and $100\,^{\circ}C$ respectively,then the temperature $\varphi$ of the interface is......... $^oC$.

Medium

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Three rods of the same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown in the figure with their ends at $100\,^{\circ}C, 50\,^{\circ}C$ and $20\,^{\circ}C$. The temperature of their junction is....... $^{\circ}C$

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

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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