Topic: Heat Transfer
A bar of Cu of length 75 cm and a steel bar of 125 cm length are joined together end to end. Both the bars are having same diameter of 2 cm. The free ends of the Cu and the steel bars are maintained at $100^{\circ}C$ and $0^{\circ}C$ respectively. The curved surfaces of the bars are thermally insulated, what is the approximate temperature at Cu-steel junction? (consider conductivity K of Cu = $400~Js^{-1}m^{-1\circ}C^{-1}$ and K for steel = $50~Js^{-1}m^{-1\circ}C^{-1}$)
- A. $\approx 95.0^{\circ}C$
- B. $\approx 93.0^{\circ}C$
- C. $\approx 90.0^{\circ}C$
- D. $\approx 89.0^{\circ}C$
Answer: B. $\approx 93.0^{\circ}C$
Explanation: For steady state heat conduction, the heat transfer rate through both bars must be equal. Let the interface temperature be $T$. Equating the heat flux: $\frac{k_{cu}(100-T)}{L_{cu}} = \frac{k_{st}(T-0)}{L_{st}}$. Substituting the given values gives $\frac{400(100-T)}{75} = \frac{50(T)}{125}$. Simplifying this yields $5.33(100 - T) = 0.4T$. Expanding gives $533 - 5.33T = 0.4T$, so $533 = 5.73T$. Solving for $T$ results in $T \approx 93.01^{\circ}C \approx 93^{\circ}C$.