Two rectangular blocks, having identical dimensions, an be arranged either in configuration-I or in configuration-II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9s to transport a certain amount of heat from the hot end to the cold end in the configuration-I. The time to transport the same amount of heat in the configuration-II is

Options

A. 2.0 s
B. 3.0 s
C. 4.5 s
D. 6.0 s

Answer

A

Explanation

`R_(1)=(L)/(kA)+(L)/(2kA)=(3L)/(2kA)`
`(1)/(R_(2))=(1)/(((L)/(kA)))+(1)/(((L)/(2kA)))=(3kA)/(L)`
`R_(2)=(1)/(3kA)`
`DeltaQ_(1)=DeltaQ_(2)`
`(DeltaT_(1))/(R_(1))t_(1)=(DeltaT_(2))/(R_(2))t_(2)`
`implies t_(2)=(R_(2))/(R_(1))t_(2)=2s`