Four rods, of different radii r and length l , are used to connect two reservoirs of heat at different temperatures. The rod that will conduct the heat fastest will be

Question

Four rods, of different radii r and length l , are used to connect two reservoirs of heat at different temperatures. The rod that will conduct the heat fastest will be (A) r=2 cm, l= text0.5 m (B) r=1cm,l= text0.5m (C) r=2cm,l= text2m (D) r=1cm,l= text1m

Tardigrade Admin · Accepted Answer

(Δ T/Δ t)=KA((Δ T/Δ x))= K(π r2)(Δ T/(l)) ∴ ((Δ Q/Δ t)) propto (r2/l) , which is maximum in this case.

Q. Four rods, of different radii $r$ and length $l$ , are used to connect two reservoirs of heat at different temperatures. The rod that will conduct the heat fastest will be

$r = 2 c m, l = 0.5 m$

$r = 1 c m, l = 0.5 m$

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

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

$\frac{Δ T}{Δ t} = K A (\frac{Δ T}{Δ x}) = K (π r^{2}) \frac{Δ T}{( l )}$
$∴ (\frac{Δ Q}{Δ t}) \propto \frac{r ^{2}}{l}$ , which is maximum in this case.

Q. Four rods, of different radii r and length l , are used to connect two reservoirs of heat at different temperatures. The rod that will conduct the heat fastest will be

r=2cm,l=0.5m

r=1cm,l=0.5m

r=2cm,l=2m

r=1cm,l=1m