Question

Two rods of aluminium and steel having the same cross-sectional area and having lengths of 80 cm and 60 cm respectively are joined as shown in the figure. The free end of the aluminium rod is at $120{}^{0}C$ and the free end of steel is at $40{}^{0}C$ and the temperature of the rod junction is $60{}^{0}C$. Then what will be the ratio of thermal conductivity of aluminium to that of steel?

• A. $\frac{6}{4}$
• B. $\frac{5}{9}$
• C. $\frac{8}{9}$
• D. $\frac{4}{9}$

Answer 1

The correct option is D $\frac{4}{9}$

$H=\frac{120-60}{\frac{80}{k_{1}A}}=\frac{60-40}{\frac{60}{k_{2}A}}$

Where,
$H=$ Heat flux (Heat flown per unit area)
$k_1\text{and}{k}_2=$ Thermal conductivity of aluminium and steel respectively

$k_1\times \frac{60}{80}=k_2\times \frac{20}{60}$
$\frac{3k_1}{4}=\frac{k_2}{3}$
$\frac{k_1}{k_2}=\frac{4}{9}$