Two rectangular blocks, having identical dimensions, can 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 2 k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s 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

For two rectangular blocks `R_(1) = (l)/(kA) = 2R , R_(2) = (l)/(2kA) = R`
In configuration `1`
Equivalent thermal resistance = `3R`
In configuration `2` Equivalent thermal resistance = `(2)/(3)R`
Rate of heat flow `DeltaQ_(1) = (DeltaT)/(3R)t "and" DeltaQ_(2) = (DeltaT)/((2R)/(3))t_(2)`
`implies (DeltaT)/(3R)t_(1) = (3DeltaT)/(2R)t_(2) implies t_(2) = (2)/(9)t_(1) = 2 "sec"`.