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

Options

A. `K_(1)A_(1)= 4K_(2)A_(2)`
B. `K_(1) A_(1) = 2K_(2)A_(2)`
C. `4K_(1)A_(1)= K_(2)A_(2)`
D. `K_(1)A_(1)= K_(2)A_(2)`

Answer

A

Explanation

Let L be length of each rod. Rate of heat flow in rod 1 for the temperature difference `Delta T` is `H_(1) =(K_(1)A_(1) Delta T)/(L)`
Rate of heat flow in rod 2 for the same difference `Delta T` is `H_(2)= (K_(2)A_(2) Delta T)/(L)`
As per question, `H_(1) = 4H_(2)`
`:. (K_(1)A_(1) Delta T)/(L) = 4(K_(2) A_(2) Delta T)/(L) or K_(1) A_(1) = 4K_(2) A_(2)`