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
$R=\frac{l}{KA}$
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, $A_1=A_2,K_1:K_2=5:4$
$\therefore \frac{d_1}{d_2}=\frac{K_1{A}_1}{K_2{A}_2}=\frac{5}{4}$