What is the length of bar B for steady state conditions? Two rods, one made of metal A that has a conductivity 400 J/s*m and a length 10 cm and...

To get the answer here we need to ensure that the rates of heat
flow through both the rods are equal else steady state conditions will not be reached. Now, we
see that the conductivity of the two rods is different. Let us denote the length of the rod of
metal B by Lb.

Now we use the equation for heat flow through the
rods, and equate them.

ka*A*(100 – T)/ 10 = kb*A*(0 – T)/
Lb

=> Lb (ka*A*(100 – T)) = 10 (kb*A*(T–
0))

=> Lb (400*A*(100 – 25)) = 10 (50*A*(25–
0))

=> Lb (8 * 75) =
10*25

=> Lb = 10*25 /
8*75

=> Lb = 5/12 cm

Notice that
rod B is much shorter than rod A. This is explained by the fact that the conductivity of A is a
lot higher than that of B.

Therefore the length of the
second rod should be 5/12 cm.