Question

Two rods of equal length have same temperature differences between their ends. If their thermal conductivities are K1 & K2 & their areas of cross section are A1 &A2 respectively,find the condition that will ensure equal rates of flow of heat through both the rods.

Answer 1

Here,
CSA of first rod = C
CSA of first rod = D
Thermal Conductivity of first wire = a
Thermal Conductivity of 2nd wire = b
Let the length of the two wires be L
Temperature difference at the ends be ∆T
Now by law thermal conduction for first conductor
∆Q/∆t = -aC(∆T)/L ---1.
For 2nd conductor
∆Q/∆t = -bD(∆T)/L ---2.
Now to have same rate, we equate eqn. 1 and eqn. 2
=> -aC(∆T)/L = -bD(∆T)/L
=> aC = bD
is the reqd. condition