Question

The ratio of the coefficient of thermal conductivity of two different materials is $5:3.$ If the thermal resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be

• A. 3 : 5
• B. 5 : 3
• C. 3 : 4
• D. 3 : 2

Answer 1

Answer: (B)

The thermal resistance of a rod of length $l$, area of cross-section $A$ and thermal conductivity $K$, is
$R=\frac{l}{KA}$
Given, thermal resistance of rods is equal therefore, also $A_1=A_2$
$\frac{l_1}{K_1{A}_1}=\frac{l_2}{K_2{A}_2}$
$\Rightarrow \frac{l_1}{K_1}=\frac{l_1}{K_2}$
$\Rightarrow \frac{l_1}{l_2}=\frac{K_1}{K_2}=\frac{5}{3}$