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. How much total heat flows through the two rods each minute? The thermal conductivity of silver is 417 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ and that of gold is 291 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$

Question

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. How much total heat flows through the two rods each minute? The thermal conductivity of silver is 417 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ and that of gold is 291 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$

Quizplus · Accepted Answer

The heat flow through the rods can be calculated using the formula $ Q = \frac{k \cdot A \cdot \Delta T \cdot t}{L} $. For silver, $ Q_{silver} = \frac{417 \cdot 0.0004 \cdot 100 \cdot 60}{0.05} \approx 20016 \, \text{J} $. For gold, $ Q_{gold} = \frac{291 \cdot 0.0004 \cdot 100 \cdot 60}{0.05} \approx 13968 \, \text{J} $. Since the rods are in series, the heat flow is limited by the rod with the lower conductivity, which is gold. Therefore, the total heat flow is approximately 8.2 kJ.

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

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