# Thermodynamics Problem 1.55 Solution: Hot/Cold Copper Rod

• xCuzIcanx
In summary: The left end is warmer than the right end, but they're both at equilibrium. The middle is also at equilibrium.
xCuzIcanx

## 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

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.

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

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.

## 1. What is the purpose of "Thermodynamics Problem 1.55 Solution: Hot/Cold Copper Rod"?

The purpose of this thermodynamics problem is to calculate the temperature distribution in a copper rod that is heated at one end and cooled at the other end.

## 2. How is the temperature distribution in the copper rod calculated?

The temperature distribution is calculated using the heat transfer equation and the boundary conditions given in the problem. This involves solving a mathematical equation to determine the temperature at different points along the rod.

## 3. Why is the copper rod heated at one end and cooled at the other end?

This setup is meant to simulate a real-life scenario where heat is transferred from a hot source to a cold sink through a conducting material, such as a copper rod. This allows us to study the temperature distribution and heat transfer characteristics of the rod.

## 4. How does the thermal conductivity of copper affect the temperature distribution in the rod?

The thermal conductivity of copper is an important factor in determining the temperature distribution in the rod. A higher thermal conductivity means that heat can be transferred more easily through the material, resulting in a more uniform temperature distribution along the rod.

## 5. What are some real-life applications of studying the temperature distribution in a copper rod?

Some real-life applications include understanding the behavior of heat transfer in various engineering systems, such as heat exchangers, and designing more efficient cooling systems for electronics. It can also help in predicting and preventing thermal failures in industrial processes.