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

Thermal resistance is inversely proportional to thermal conductivity, hence thermal resistance of individual blocks can be assumed as 2R and R respectively.
For configuration 1, `R_1 ` = 3R,
For configuration 2,` R_2 = 2/3 R`
For the same temperature difference heat current is inversely proportional to the thermal resistance, hence ratio of heat currents can be written as follows:
`(Q_1)/(Q_2) = (1)/(3R). 2/3 R = 2/9`
` Q_1t_1 = Q_2t_2`
` rArr t_2 =Q_1/Q_2 t_1 = 2/9 xx 9 = 2 sec `