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. (a)2.0 s
B. (b)3.0 s
C. (c)4.5 s
D. (d).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)=(L)/(3KA)`
Now `DeltaQ_(1)=DeltaQ_(2),(DeltaT)/(R_(1))t_(1)=(DeltaT)/(R_(2))
rArrt_(2)=(R_(2))/(R_(1))t_(1)=2s`