Which of the following circular rods, (given radius r and length l) each made of the same material and whose ends are maintaind at the same temperature diff. will conduct most heat ?

Options

A. `r=2r_(o)l=2l_(o)`
B. `r=r_(o),l=2l_(o)`
C. `r=2r_(o),l=l_(o)`
D. `r=r_(o),l=l_(o)`

Answer

C

Explanation

`(dQ)/(dt)=kA(dT)/(dx)` since `A=pir^(2)` and `dx=l`
`:.(dQ)/(dt)prop(r^(2))/(l)`
Now `(r^(2))/(l)` will be maximum, when `r=2r_(0)` and `l=l_(0)`
`:.` Correct choice is (c ).