(A) Let the thermal conductivity of steel be $K_{steel} = k$. Then,the thermal conductivity of copper is $K_{copper} = 9k$. Let the temperature of the

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(A) Let the thermal conductivity of steel be $K_{steel} = k$. Then,the thermal conductivity of copper is $K_{copper} = 9k$. Let the temperature of the junction be $\theta$. Since the rods are in series and insulated from the surroundings,the rate of heat flow $(H)$ through both rods must be equal in steady state. $H = \frac{K_{copper} A (100 - \theta)}{L/2} = \frac{K_{steel} A (\theta - 0)}{L/2}$ Since the cross-sectional area $A$ and length $L/2$ are the same for both: $K_{copper} (100 - \theta) = K_{steel} (\theta - 0)$ $9k (100 - \theta) = k \theta$ $900 - 9\theta = \theta$ $10\theta = 900$ $\theta = 90\,^oC$.

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

Medium

$A$ large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $(\frac{L}{2})$ each. The rods are completely insulated from the surroundings. If the free end of the copper rod is maintained at $100\,^oC$ and that of the steel rod at $0\,^oC$,then the temperature of the junction is........$^oC$ (Thermal conductivity of copper is $9$ times that of steel).

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A
$90$
B
$50$
C
$10$
D
$67$

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10-2.Heat Transfer

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$A$ copper rod of length $10 \ cm$ and cross-sectional area $100 \ cm^2$ is to conduct $4000 \ J/s$ of heat. The thermal conductivity of copper is $400 \ W/m \cdot ^\circ C$. The temperature difference between the two ends of the rod must be maintained at ............. $^\circ C$.

There are two identical vessels filled with equal amounts of ice. The vessels are made of different metals. If the ice melts in the two vessels in $20$ and $35$ minutes respectively,the ratio of the coefficients of thermal conductivity of the two metals is:

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