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 $385\, Js^{-1}m^{-1}K^{-1}$ and steel is $50 \,Js^{-1}m^{-1}K^{-1}.$ 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) =50 T $
$\Rightarrow 385 \times 100 =(385+50) T $
$\Rightarrow T= \frac{385 \times 100}{435} \approx 88^{\circ} C$