Question

The ratio of thermal conductivities of two rods of different materials is $5:4$. The two rods have the same area of cross-section and the same thermal resistance. They will have the lengths in the ratio

• A. $4 :5$
• B. $9 :1$
• C. $1 :9$
• D. $5 :4$

Answer 1

Answer: (D)

The thermal resistance $R$ is given by
$R=\frac{l}{K A}$
where $l$ is length of conducting material, $K$ the coefficient of thermal conductivity, $A$ the area
Given, $R_{1} =R_{2}$
$\frac{K_{1} A_{1}}{d_{1}} =\frac{K_{2} A_{2}}{d_{2}}$
Given, $ A_{1}=A_{2}, K_{1}: K_{2}=5: 4$
$\therefore \frac{d_{1}}{d_{2}}=\frac{K_{1} A_{1}}{K_{2} A_{2}}=\frac{5}{4}$