Solve Heat Current Problem at Junction of Copper, Brass & Steel Rods

In summary, the problem involves welding three different rods (copper, brass, and steel) together to form a Y-shaped figure. The cross-sectional area of each rod is 2.00 cm^2 and the lengths are given as 13.0 cm for copper, 18.0 cm for brass, and 24.0 cm for steel. The free end of the copper rod is maintained at 100.0 degrees C and the free ends of the brass and steel rods are at 0.0 degrees C. The goal is to determine the temperature at the junction where the three rods meet. The heat current formula is used, but the usual method of solving with two bars will not work for three bars.
  • #1
sdoug041
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Homework Statement



Rods of copper, brass, and steel are welded together to form a Y-shaped figure. The cross-sectional area of each rod is 2.00 cm^2. The free end of the copper rod is maintained at 100.0 degrees C, and the free ends of the brass and steel rods at 0.0 degrees C. Assume there is no heat loss from the surfaces of the rods. The lengths of the rods are: copper, 13.0 cm; brass, 18.0 cm; steel, 24.0 cm

What is the temperature at the junction?

Homework Equations



H = kA(T[hot]-T[cold]) / L

Where H is the heat current, k is the materials thermal conductivity, A is the cross-sectional area,
T[hot]-T[cold] / L is the temperature gradient. (change in temp divided by length).

The Attempt at a Solution



I can solve these types of questions with only 2 bars. What I would do is plug in the values for each material into the heat current formula , make them equal each other, then solve for T at the junction. This method won't work for 3 materials coming together. Please help! Thanks.[Edit] I'm sorry for posting this in the advanced physics thread it was supposed to be in introductory. If any mod sees this they can move it, thank you!
 
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  • #2
Can you show where you're getting stuck? It looks like you're going to have four equations and four unknowns.
 

1. What is the heat current problem at the junction of copper, brass, and steel rods?

The heat current problem at the junction of copper, brass, and steel rods refers to the challenge of efficiently transferring heat between these three different types of materials. When these rods are connected, heat can be lost due to the differences in thermal conductivity and specific heat capacities of each material, leading to an inefficient transfer of heat.

2. How can this heat current problem be solved?

To solve this heat current problem, one approach is to use a material with high thermal conductivity, such as copper, at the junction point. This will help to distribute the heat more evenly and effectively between the three rods. Additionally, using insulating materials or coatings can help to reduce heat loss at the junction.

3. What factors affect the heat current at the junction of these rods?

There are several factors that can affect the heat current at the junction of these rods, including the thermal conductivity and specific heat capacity of each material, the length and diameter of the rods, the temperature difference between the rods, and any insulating materials or coatings used.

4. How can the efficiency of heat transfer be improved at the junction of these rods?

To improve the efficiency of heat transfer at the junction, it is important to minimize the temperature difference between the rods. This can be achieved by using materials with similar thermal properties, minimizing the length and diameter of the rods, and using insulating materials or coatings to reduce heat loss.

5. Are there any potential challenges or limitations to solving this heat current problem?

One potential challenge is finding a balance between cost and efficiency. Using high-quality materials or coatings may improve heat transfer, but they may also be more expensive. Additionally, the design and placement of the rods can also impact the efficiency of heat transfer. Careful consideration and testing may be necessary to optimize the solution for a specific application.

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