Ratio of coefficient of thermal conductivity of two different material

1.	Ratio of coefficient of thermal conductivity of two different materials is 3 : 2. What should be the ratio of their lengths to have same thermal resistance of the two rods of these material of equal thickness?
Answer» Since, thermal resistance, R = \(\frac{1}{KA}\). For equal thermal resistance \(\frac{l_1}{K_1A_1}=\frac{l_2}{K_2A_2}\) with equal thickness A₁ = A₂. Here \(\frac{l_1}{k_1}=\frac{l_2}{k_2}\) = \(\frac{l_1}{l_2}=\frac{K_1}{K_2}=\frac{3}{2}\) i.e., l₁:l₂ = 3: 2

Ratio of coefficient of thermal conductivity of two different materials is 3 : 2. What should be the ratio of their lengths to have same thermal resistance of the two rods of these material of equal thickness?

Answer»

Since, thermal resistance,

R = \(\frac{1}{KA}\). For equal thermal resistance \(\frac{l_1}{K_1A_1}=\frac{l_2}{K_2A_2}\) with equal thickness A₁ = A₂.

Here \(\frac{l_1}{k_1}=\frac{l_2}{k_2}\)

= \(\frac{l_1}{l_2}=\frac{K_1}{K_2}=\frac{3}{2}\)

i.e., l₁:l₂ = 3: 2