Question

A rod is of 40 cm in length and has a temperature difference of 80${}^o$C at its two ends. Another rod B is of length 60 cm and has a temperature difference of 90${}^o$C, but has the same area of cross section. If the rate of flow of heat is the same, then the ratio of their thermal conductivities will be :

• A. $3:4$
• B. $4:3$
• C. $1:2$
• D. $2:1$

Answer 1

Answer: (A)

$3:4$

$Q=\frac{KA\Delta T}{l}$

$\frac{K_1\Delta T_1}{l_1}=\frac{K_2\Delta T_2}{l_2}$

$\frac{K_1}{K_2}=\frac{{\Delta T}_2{l}_1}{{\Delta T}_1{l}_2}$

$\frac{K_1}{K_2}=\frac{90\times 40}{80\times 60}=\frac{3}{4}$