The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and the other brass) are joined together end to end in excellent thermal contact. The rods are of equal lengths and radii. The free end of the brass rod is maintained at 0°C and the aluminum's free end is heated to 200°C. If no heat escapes from the sides of the rods, what is the temperature at the interface between the two metals?

Question

Quizplus · Accepted Answer

The temperature at the interface can be found using the concept of thermal resistance, which is inversely proportional to thermal conductivity. Since the thermal conductivity of aluminum is twice that of brass, the thermal resistance of the aluminum rod is half that of the brass rod. This means the temperature drop across the aluminum rod is half that across the brass rod. Given a total temperature difference of 200°C, the temperature drop across the brass rod is two-thirds of this (since it has twice the thermal resistance of the aluminum rod, making a total of three parts), and the drop across the aluminum rod is one-third. Therefore, the temperature at the interface is 200°C - (200°C / 3) = 133°C.

The Thermal Conductivity of Aluminum Is Twice That of Brass