Question

Two rods, one made of copper and the other steel of the same length and cross sectional area are joined together. (The thermal conductivity of copper is $385J.s^{-1}.m^{-1}.K^{-1}$ and steel is $50J.s^{-1}.m^{-1}.K^{-1}.)$ If the copper end is held at ${100}^{\circ }C$ and the steel end is held at $0^{\circ }C$, what is the junction temperature (assuming no other heat losses)?

• A. ${12}^{\circ }C$
• B. ${50}^{\circ }C$
• C. ${73}^{\circ }C$
• D. ${88}^{\circ }C$

Answer 1

The correct option is D ${88}^{\circ }C$

Let the length and area of each rod be $l$ and $A$, respectively.

Also the temperature at the junction be $T$.

Given : $K_c=385J{s}^{-1}{m}^{-1}{K}^{-1}$ $K_s=50J{s}^{-1}{m}^{-1}{K}^{-1}$

As the two rods are connected in series with each other, thus rate of heat flow through the rods must be equal i.e. $Q_c=Q_s$

$\therefore$ $\frac{K_{c}A(100-T)}{l}=\frac{K_{s}A(T-0)}{l}$

Or $K_c(100-T)=K_s(T-0)$

Or $385(100-T)=50T$

Or $435T=38500$

$⟹$ $T={88}^{o}C$