The ratio of the thermal conductivity of two | vedclass

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Question

(B) The thermal resistance $R_{th}$ of a rod is given by the formula $R_{th} = \frac{L}{kA}$, where $L$ is the length, $k$ is the thermal conductivity

Vedclass · Accepted Answer

$6:5$

Vedclass · Answer

(B) The thermal resistance $R_{th}$ of a rod is given by the formula $R_{th} = \frac{L}{kA}$, where $L$ is the length, $k$ is the thermal conductivity, and $A$ is the area of cross-section.Given that the two rods have the same thermal resistance $(R_{th1} = R_{th2})$ and the same area of cross-section $(A_1 = A_2 = A)$, we have:$\frac{L_1}{k_1 A} = \frac{L_2}{k_2 A}$This simplifies to $\frac{L_1}{k_1} = \frac{L_2}{k_2}$, or $\frac{L_1}{L_2} = \frac{k_1}{k_2}$.Given the ratio of thermal conductivities is $\frac{k_1}{k_2} = \frac{6}{5}$, it follows that the ratio of their lengths is $\frac{L_1}{L_2} = \frac{6}{5}$.

The ratio of the thermal conductivity of two rods of different materials is $6:5$. The two rods of same area of cross section and same thermal resistance will have the lengths in the ratio:

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