Four rods of the same material with different radii r and length l are used to connect two heat reservoirs at different temperature. Which one will conduct most heat?

Question

Four rods of the same material with different radii r and length l are used to connect two heat reservoirs at different temperature. Which one will conduct most heat? (A) r=1 cm, l=1 m (B) r=1 cm, l=(1/2)m (C) r=2 cm, l=2 m (D) r=2 cm, l=(1/2)m

Tardigrade Admin · Accepted Answer

Rate of heat flow propto (A Δ T/l) A rod maintained at temperature difference (Tl - T2) will have heat conduction rate =(d Q/d t) (d Q/d t)=(K A (T1 - T2)/l) In given option, r=2cm and l=(1/2)m will conduct most heat.

Q. Four rods of the same material with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperature. Which one will conduct most heat?

$r = 1 c m, l = 1 m$

$r = 1 c m, l = \frac{1}{2} m$

$r = 2 c m, l = 2 m$

$r = 2 c m, l = \frac{1}{2} m$

Rate of heat flow $\propto \frac{A Δ T}{l}$
A rod maintained at temperature difference $(T_{l} - T_{2})$ will have heat conduction rate $= \frac{d Q}{d t}$
$\frac{d Q}{d t} = \frac{K A ( T _{1} - T _{2} )}{l}$
In given option, $r = 2 c m$ and $l = \frac{1}{2} m$ will conduct most heat.

Q. Four rods of the same material with different radii r and length l are used to connect two heat reservoirs at different temperature. Which one will conduct most heat?

r=1cm,l=1m

r=1cm,l=21​m

r=2cm,l=2m

r=2cm,l=21​m