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

Options

A. `r=2r_(0),l=2l_(0)`
B. `r=2r_(0),l=l_(0)`
C. `r=r_(0),l=2l_(0)`
D. `r=r_(0),l=l_(0)`

Answer

B

Explanation

We know that `Q=(T_(H)-T_(L))/(R )`
Also Thermal resistance, `R=(l)/(KA)=(l)/(K pi r^(2))`
Heat flow will maximum when thermal resistance is minimum. From given option
(i) `r=2r_(0), l=2l_(0) therefore R=(2l_(0))/(Kpi (2r_(0))^(2))=(l_(0))/(2Kpi r_(0)^(2))`
(ii) `r=2r_(0), l=l_(0) therefore R=(l_(0))/(K pi (2r_(0))^(2))=(l_(0))/(4Kpi r_(0)^(2))`
(iii) `r=r_(0), l=2l_(0) therefore R=(2l_(0))/(Kpi r_(0)^(2))=(2l_(0))/(Kpi r_(0)^(2))`
(iv) `r=r_(0), l=l_(0) therefore R=(l_(0))/(Kpi r_(0)^(2))=(l_(0))/(Kpi r_(0)^(2))`
It is clear that for option (b) resistance is minimum, hence heat flow will bc maximum.