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(B) The rate of heat flow $\dot{Q}$ through a rod is given by the formula: $\dot{Q} = \frac{KA \Delta T}{l}$.Here,$K$ is the thermal conductivity,$A$

Vedclass · Accepted Answer

$3 K_1 A_1 = K_2 A_2$

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(B) The rate of heat flow $\dot{Q}$ through a rod is given by the formula: $\dot{Q} = \frac{KA \Delta T}{l}$.Here,$K$ is the thermal conductivity,$A$ is the cross-sectional area,$\Delta T$ is the temperature difference,and $l$ is the length of the rod.Given that the length $l$ and temperature difference $\Delta T$ are the same for both rods $P$ and $Q$,the rate of heat flow is directly proportional to the product $KA$.According to the problem,the rate of heat flow through rod $Q$ is three times that of rod $P$:$(\dot{Q})_Q = 3 (\dot{Q})_P$Substituting the formula:$\frac{K_2 A_2 \Delta T}{l} = 3 \left( \frac{K_1 A_1 \Delta T}{l} \right)$Since $l$ and $\Delta T$ are equal,they cancel out from both sides:$K_2 A_2 = 3 K_1 A_1$ or $3 K_1 A_1 = K_2 A_2$.

Two metal rods $P$ and $Q$ have the same length and the same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$,and their cross-sectional areas are $A_1$ and $A_2$ respectively. If the rate of flow of heat through rod $Q$ is three times that in rod $P$,then:

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