Question

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $ K_1$ and $K_2 $ and cross sectional areas $ A_1 $ and $ A_ 2 $ respectively. If the rate of heat conduction in 1 is four times that in 2, then :

• A. $ K _1A_1 = 4K_2A_2$
• B. $ K_1A_1= 2K_2A_2$
• C. $ 4K_1A_1= K_2A_2$
• D. $ K_1A_1= K_2A_2$

Answer 1

The Correct Option is A

(a): Let L be length of each rod.
Rate of heat flow in rod 1 for the temperature
difference $ \Delta T $ is
$H_1 = \frac{ K_1A_1 \Delta T }{ L}$
Rate of heat flow in rod 2 for the same difference
$ \Delta T $ is
$ H_2 = \frac{ K _2A_2 \Delta T }{ L} $
As per question
$ H_1 = 4H_2$
$ \frac{K_1A_1 \Delta T }{ L } = 4 \frac{K_2A_2 \Delta T }{ L }$
$ K_1A_1= 4K_2A_2$