Question

Two rods, one made of copper and the other steel of the same length and cross-sectional are a 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 $100°C$ and the steel end is held at $0°C,$ what is the junction temperature? (Assuming no other heat losses)

• A. $12°C$
• B. $50°C$
• C. $73°C$
• D. $88°C$

Answer 1

Answer: (D)

Let junction temperature is $T°C$.

Then, assuming no heat loss and steady state,
Heat flow through copper rod per second = Heat flow through steel rod per second
$\Rightarrow \frac{K_{\text{Copper }}A(100-T)}{l}=\frac{K_{\text{steel }}A(T-0)}{l}$
$\Rightarrow K_{\text{Copper }}(100-T)=K_{\text{steel }}\cdot T$
$\therefore$ Area and length of both rods are equal.
Substituting values, we get
$385(100-T)=50T$
$\Rightarrow 385\times 100=(385+50)T$
$\Rightarrow T=\frac{385\times 100}{435}\approx 88^{\circ }C$