Two metal rods of same length have same temperature difference between their ends. Their thermal conductivities are `K_(1)` and `K_(2)` and cross-sections `A_(1)` and `A_(2)` respectively. What is the condition for the same rates of flow of heat ?

Options

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

Answer

D

Explanation

`(Q_(1))/(t)=(k_(1)A_(1)(T_(1)-T_(2)))/(d)`
`(Q_(2))/(t)=(k_(2)A_(2)(T_(1)-T_(2)))/(d)`
Now `(Q_(1))/(t)=(Q_(2))/(t)`
`rArr(k_(1)A_(1)(T_(1)=T_(2)))/(d)=(k_(1)A_(2)(T_(1)-T_(2)))/(d)`
`rArr" "(k_(1))/(k_(2))=(A_(2))/(A_(1))`
Thus correct choice is (b)