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

Answer

A

Explanation

(a) Given `H_I=H_(II)`
`k_1(ADeltaT)/(l+l)xxt_1=k_2((A+A)DeltaT)/lxxt_2`
`:. T_2=(k_1)/(k_2)xx(t_1)/4…….(i)`
Where `k_1 and k_2` are the equivalent conductivities in
configuration I and II respectively.
For configuration I:
`(l+l)/(k_1)=l/K+l/(2K) :. 2/(K_1)=3/(2k)`
`:. K_1=(4k)/3.....(ii)` For configuration II:
`k_2(A+A)=kA+2kA`
`:. k_2=(3k)/2......(iii)`
From (i) , (ii)and (iii) `t_2=((4k)/3)/((3k)/2)xx9/4=2sec`
option (a) is correct