Discussion Forum

1)

Two  rectangular blocks , having indentical dimensions, can be arranged either in configuration 1 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 configuratiuons. 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

Answer:

Option A

Explanation:

$R_{1}=R_{1}+R_{2}=\left(\frac{l}{KA}\right)+\left(\frac{l}{2KA}\right)=\frac{3}{2}\left(\frac{l}{KA}\right)$

$\frac{1}{R_{II}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}=\frac{KA}{l}+\frac{2KA}{l}$

or   $R_{II}=\frac{l}{3KA}=\frac{R_{1}}{4.5}$

since thermal resistance R_II is 4.5 times less than thermal resistance R₁

$\therefore$    $t_{II}=\frac{t_{I}}{4.5}=2 s$