Four rods with different raddi r and length l are used to connect two heat reservoirs at different temperatures . Which one will conduct most heat ?

Options

A. `r=1cm,l=1m`
B. `r=1cm,l=(1)/(2)m`
C. `r=2cm,l=2m`
D. `r=2cm,l=(1)/(2)m`

Answer

D

Explanation

`H=(KAd theta)/(L)prop(A)/(L)=(pir^(2))/(L)`
`((A)/(L))_(1)=(pi(1)^(2))/((1)/(2))=2pi" units"((A)/(L))_(2)=(pi(1)^(2))/((1)/(2))=2pi" units"`
`((A)/(L))_(3)=(pi(2)^(2))/((1)/(2))=4pi" units"((A)/(L))_(4)=(pi(2)^(2))/((1)/(2))=8pi" units"`
So rod (4) will conduct most heat per second.