Question

Three rods each of same length and cross section are joined in series. The thermal conductivity of the materials are k, 2k, and 3k respectively. if one end is kept at ${200}^{\circ }C$. What would be the temperature between the junction of 2k and 3k in the steady state? Assume that no heat is lost to radiation form the sides of the rods.

Answer 1

Given,

$H_1=H_2=H_3$

$\therefore \frac{200-{\theta }_1}{\frac{l}{KA}}=\frac{{\theta }_1-{\theta }_2}{\frac{l}{2KA}}=\frac{{\theta }_2-100}{\frac{l}{3KA}}$

solving the above equation, we get,

${\theta }_1={145.5}^{\circ }C$

${\theta }_2={118}^{\circ }C$