Two rods P and Q of equal lengths have thermal conductivities `K_(1) and K_(2)` and cross-sectional areas `A_(1) and A_(2)` respectively. If the temperature difference across the ends of each rod is the same, then the condition for which the rate of flow of heat through each of them will be equal, is

Options

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

Answer

A

Explanation

`((DeltaQ)/(Deltat))_(P) = ((DeltaQ)/(Deltat))_(Q`
`K_(1)A_(1)(T_(1)-T_(2))/t = K_(2)A_(2) (T_(1) - T_(2))/l`
or `K_(1)A_(1) = K_(2)A_(2)` or `A_(1)/A_(2) = K_(2)/K_(1)`