A cylindrical rod having temperature `T_(1)` and `T_(2)` at its end. The rate of flow of heat is `Q_(1)("Cal")/(s)` If all linear dimensions are doubled keeping temperature constant, then the rate of flow of heat `Q_(2)` in `("Cal")/(s)` will be . . . . . . . .

Options

A. `4Q_(1)`
B. `2Q_(1)`
C. `(Q_(1))/(4)`
D. `(Q_(1))/(2)`

Explanation

Heat flow rate,
In `H=ka((T_(1)-T_(2))/(L)), k(T_(1)-T_(2)) and pi` constant
`:.H prop (r^(2))/(L) " " [ : A= pi r^(2)]`
`:.(H_(2))/(H_(1))=(r_(2))/(r_(1))xx(L_(1))/(L_(2))`
`r_(2)=r_(1)`
`L_(2)= 2L_(1)`
`H prop (L_(2))/(L_(1))`
`(H_(1))/(H_(2))=(L_(2))/(L_(1))`
`(Q)/(H_(2))=(2L_(1))/(L_(1))`
`H_(2)=(Q)/(2)`