(A) In the steady state,the rate of heat flow through block $A$ must be equal to the rate of heat flow through block $B$.Let $K_1$ and $K_2$ be the th

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(A) In the steady state,the rate of heat flow through block $A$ must be equal to the rate of heat flow through block $B$.Let $K_1$ and $K_2$ be the thermal conductivities of blocks $A$ and $B$ respectively,$L$ be their length,and $A$ be their cross-sectional area.Given: $\frac{K_1}{K_2} = \frac{1}{3}$,so $K_2 = 3K_1$.Let $\theta$ be the temperature of the junction.The rate of heat flow is given by $H = \frac{KA(\Delta T)}{L}$.Equating the heat flow rates: $\frac{K_1 A (100 - \theta)}{L} = \frac{K_2 A (\theta - 0)}{L}$.Since $A$ and $L$ are the same for both,we have $K_1(100 - \theta) = K_2\theta$.Substituting $K_2 = 3K_1$: $K_1(100 - \theta) = 3K_1\theta$.$100 - \theta = 3\theta$.$100 = 4\theta$.$\theta = 25^{\circ}C$.

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

Medium

Two rectangular blocks $A$ and $B$ of different metals have the same length and the same area of cross-section. They are kept in such a way that their cross-sectional areas touch each other. The temperature at one end of $A$ is $100^{\circ}C$ and that of $B$ at the other end is $0^{\circ}C$. If the ratio of their thermal conductivities is $1 : 3$,then under steady state,the temperature of the junction in contact will be ........ $^{\circ}C$.

A
$25$
B
$50$
C
$75$
D
$100$

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10-2.Heat Transfer

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Heat Conduction and Thermal Conductivity

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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The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$. The rate of heat transfer,$\frac{dQ}{dt}$ through the rod in a steady state is given by:

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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......... $^oC$.

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$A$ wall consists of two layers $A$ and $B$. The two layers have the same thickness but are made of different materials. The thermal conductivity of $A$ is twice that of $B$. Under steady-state conditions,the temperature difference between the two ends is $36 ^\circ C$. The temperature difference across the two surfaces of $A$ is .......... $^\circ C$.

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$A$ cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod,when placed in thermal contact with the two reservoirs in time $t$?

MediumAIPMT 2010

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The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$. The rate of heat transfer,$\frac{dQ}{dt}$ through the rod in a steady state is given by:

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