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  4. Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their thermal conductivities are K1 and K2 and cross sectional areas A1 and A 2 respectively. If the rate of heat conduction in 1 is four times that in 2, then :

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Q. 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 :

NEETNEET 2013Thermal Properties of Matter

Solution:

(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$