Thermodynamics Problem 1.55 Solution: Hot/Cold Copper Rod

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Discussion Overview

The discussion revolves around a thermodynamics problem involving a cylindrical copper rod that is insulated on its lateral surface while its ends are in contact with hot and cold walls. Participants explore the temperature distribution along the rod when it reaches thermal equilibrium, addressing specific questions about the behavior of temperature at various points along the rod.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • Some participants note that if the rod is in equilibrium, the temperature should stabilize and not fluctuate.
  • There is a suggestion that due to the symmetry and uniformity of the copper material, heat conductivity remains constant from end to end, prompting questions about how temperature varies along the rod.
  • One participant proposes that the temperature should be warm past a certain point towards the right end of the rod, suggesting a non-uniform temperature distribution.
  • Another participant requests clarification on the temperature profile, asking for a sketch to illustrate the proposed temperature distribution from the left end to the right end of the rod.
  • A later reply emphasizes that "equilibrium" implies every part of the rod should be at a constant temperature, which raises questions about the proposed temperature variations.

Areas of Agreement / Disagreement

Participants express differing views on the temperature distribution along the rod, with some suggesting a uniform temperature due to equilibrium, while others propose a varying temperature profile based on heat conductivity. The discussion remains unresolved regarding the exact nature of the temperature distribution.

Contextual Notes

Participants have not provided specific equations or detailed mathematical analysis to support their claims, and assumptions regarding the uniformity of the material and heat conductivity are not fully explored.

xCuzIcanx
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xCuzIcanx said:

Homework Statement



http://books.google.com/books?id=oy...re in contact with hot and cold walls&f=false

the problem is number 1.55

Homework Equations



No equations

The Attempt at a Solution


Well I know that if it's in equilibrium that means the temperature of the rod should stop fluctuating. But I don't understand questions a. and exactly how to do it.

You can argue from symmetry and uniformity of the material (copper cylinder) that the heat conductivity is constant from end to end of the rod. If so, how will the temperature vary along the rod? What's the temperature at the left end? How about the right end? The middle?
 
gneill said:
You can argue from symmetry and uniformity of the material (copper cylinder) that the heat conductivity is constant from end to end of the rod. If so, how will the temperature vary along the rod? What's the temperature at the left end? How about the right end? The middle?

Wait, so if it's uniform and the heat conductivity is constant then shouldn't the temperature of the rod be warm past x to the right and be at it's equilibrium a little bit past the center towards the right?
 
xCuzIcanx said:
Wait, so if it's uniform and the heat conductivity is constant then shouldn't the temperature of the rod be warm past x to the right and be at it's equilibrium a little bit past the center towards the right?

Your description is not clear to me. Can you sketch the temperature profile you're picturing? Start at the left end of the rod and finish at its right end.
 
xCuzIcanx said:
Wait, so if it's uniform and the heat conductivity is constant then shouldn't the temperature of the rod be warm past x to the right and be at it's equilibrium a little bit past the center towards the right?

"Equilibrium" means every part of the rod is at a constant temperature.