The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and the other brass) of the same length and cross-sectional area are joined together end to end. The free end of the brass rod is maintained at $0 ^ { \circ } \mathrm { C }$ and the free end of the aluminum rod is maintained at $200 ^ { \circ } \mathrm { C }$ If no heat escapes from the sides of the rods, what is the temperature at the place where the two rods are joined together?

Question

Quizplus · Accepted Answer

The temperature at the junction can be found using the concept of thermal resistance, which is inversely proportional to thermal conductivity. Since aluminum has twice the thermal conductivity of brass, it will have half the thermal resistance. This means heat flows more easily through aluminum than brass. Given the linear temperature gradient and the properties of the materials, the temperature at the junction will be closer to the temperature of the brass end due to its higher thermal resistance. By setting up the proportion based on thermal resistances and the given temperatures, the temperature at the junction is calculated to be $133 ^ { \circ } \mathrm { C }$, making option B correct.

The Thermal Conductivity of Aluminum Is Twice That of Brass 0∘C0 ^ { \circ } \mathrm { C }0∘C

The Thermal Conductivity of Aluminum Is Twice That of Brass $0 ^ { \circ } \mathrm { C }$