Question

Two rods with the same dimensions have thermal conductivities in the ratio $1:2$. They are arranged between heat reservoirs with the same temperature difference, in two different configurations, A and B. The rates of heat flow in A and B are $I_A$ and $I_B$ respectively. The ratio $\frac{I_A}{I_B}$ is equal to

• A. $1:2$
• B. $1:3$
• C. $2:5$
• D. $2:9$

Answer 1

The correct option is D $2:9$

Rate of heat flow $I\propto \frac{\Delta T}{R}$

$\because \Delta T$ = temperature difference is same.

$\therefore I\propto \frac{1}{\text{Thermal resistance}}$

$\frac{I_A}{I_B}=\frac{R_B}{R_A}=\frac{\left(R\right)\left(2R\right)/R+2R}{(R+2R)}=\frac{2}{9}$