Two Metal Rods, One Silver and the Other Gold, Are $100 ^ { \circ } \mathrm { C }$

Two metal rods, one silver and the other gold, are attached to each other end-to-end. The free end of the silver rod is immersed in a steam chamber at $100 ^ { \circ } \mathrm { C }$ and the free end of the gold rod in an ice water bath at $0 ^ { \circ } \mathrm { C }$ The rods are both 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the ends. What is the temperature at the point where the two rods are in contact with one another? The thermal conductivity of silver is 417 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$ and that of gold is 291 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$

A) $47 ^ { \circ } \mathrm { C }$
B) $59 ^ { \circ } \mathrm { C }$
C) $53 ^ { \circ } \mathrm { C }$
D) $41 ^ { \circ } \mathrm { C }$
E) $39 ^ { \circ } \mathrm { C }$

Correct Answer:

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