The ratio of thermal conductivity of two rods | vedclass

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Question

(A) The thermal resistance $R$ of a rod is given by the formula $R = \frac{\ell}{KA}$,where $\ell$ is the length,$K$ is the thermal conductivity,and $

Vedclass · Accepted Answer

$5 : 4$

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(A) The thermal resistance $R$ of a rod is given by the formula $R = \frac{\ell}{KA}$,where $\ell$ is the length,$K$ is the thermal conductivity,and $A$ is the cross-sectional area.Given that the thermal resistances are equal $(R_1 = R_2)$ and the areas are equal $(A_1 = A_2 = A)$:$\frac{\ell_1}{K_1 A} = \frac{\ell_2}{K_2 A}$$\frac{\ell_1}{\ell_2} = \frac{K_1}{K_2}$Given the ratio of thermal conductivities $\frac{K_1}{K_2} = \frac{5}{4}$,it follows that the ratio of their lengths is $\frac{\ell_1}{\ell_2} = \frac{5}{4}$.

The ratio of thermal conductivity of two rods of different materials is $5 : 4$. If the two rods have the same cross-sectional area and the same thermal resistance,what is the ratio of their lengths?

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