Thermodynamics Problem 1.55 Solution: Hot/Cold Copper Rod

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The discussion revolves around solving a thermodynamics problem involving a cylindrical copper rod insulated on its lateral surface, with its ends in contact with hot and cold walls. Participants emphasize that the rod will reach thermal equilibrium, meaning its temperature will stabilize and not fluctuate. The uniformity and constant heat conductivity of the copper material suggest that temperature will vary along the length of the rod, with specific temperatures at each end and a gradient in between. There is a focus on understanding how to sketch the temperature profile from one end of the rod to the other. Ultimately, clarity on the equilibrium concept is crucial for solving the problem effectively.
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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.
 

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