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
$R=\frac{l}{K A}$
Given, thermal resistance of rods is equal therefore, also $A_{1}=A_{2}$
$\frac{l_{1}}{K_{1}\, A_{1}}=\frac{l_{2}}{K_{2} \,A_{2}}$
$\Rightarrow \frac{l_{1}}{K_{1}}=\frac{l_{1}}{K_{2}}$
$\Rightarrow \frac{l_{1}}{l_{2}}=\frac{K_{1}}{K_{2}}=\frac{5}{3}$