The ratio of thermal conductivity of two rods | vedclass

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

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$5:4$

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(D) The thermal resistance $R$ of a rod is given by the formula $R = \frac{l}{KA}$,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 area of cross-section $(A_1 = A_2 = A)$ and the same thermal resistance $(R_1 = R_2 = R)$,we can write:$R_1 = \frac{l_1}{K_1 A}$ and $R_2 = \frac{l_2}{K_2 A}$.Since $R_1 = R_2$,we have $\frac{l_1}{K_1 A} = \frac{l_2}{K_2 A}$.Simplifying this,we get $\frac{l_1}{l_2} = \frac{K_1}{K_2}$.Given the ratio of thermal conductivities $\frac{K_1}{K_2} = \frac{5}{4}$,it follows that the ratio of their lengths is $\frac{l_1}{l_2} = \frac{5}{4}$.

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

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