Question

Figure shows a copper rod joined to a steel rod. The rods have equal length and equal cross-sectional area. The free end of the copper rod is kept at 0°C and that of steel rod is kept at 100°C. Find the temperature of the junction of the rod. 
Conductivity of copper = \( 390 \, \text{W/m°C} \)
Conductivity of steel = \( 46 \, \text{W/m°C} \)

• A. 18.01°C
• B. 26°C
• C. 10.6°C
• D. 20°C

Hint:

In a composite rod, the temperature at the junction can be found by equating the heat flow through each material.

Answer 1

The Correct Option is C

Step 1: Use the thermal conductivity equation.
The heat conducted through both rods is the same, so we use the formula for thermal conductivity \( Q = \frac{k A (T_2 - T_1)}{L} \), where \( k \) is the thermal conductivity, \( A \) is the area, \( L \) is the length, and \( T_1 \), \( T_2 \) are the temperatures at each end.
Step 2: Set up the equation for the temperature at the junction.
Equating the heat conducted through copper and steel, we find the temperature at the junction to be 10.6°C. Final Answer: \[ \boxed{10.6°C} \]