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

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SUMMARY

The discussion focuses on solving the heat current problem at the junction of copper, brass, and steel rods. The rods have specific lengths and cross-sectional areas, with the copper rod maintained at 100.0 degrees C and the brass and steel rods at 0.0 degrees C. The heat current equation, H = kA(T[hot]-T[cold]) / L, is essential for determining the temperature at the junction. Participants emphasize the need to set up multiple equations to account for the three materials involved, leading to a system of equations to solve for the junction temperature.

PREREQUISITES
  • Understanding of thermal conductivity and its significance in heat transfer.
  • Familiarity with the heat current equation H = kA(T[hot]-T[cold]) / L.
  • Basic knowledge of algebraic methods for solving systems of equations.
  • Concept of temperature gradients in materials.
NEXT STEPS
  • Research the thermal conductivities of copper, brass, and steel for accurate calculations.
  • Learn how to set up and solve systems of equations involving multiple variables.
  • Explore the concept of steady-state heat transfer in composite materials.
  • Study examples of heat transfer problems involving multiple materials to reinforce understanding.
USEFUL FOR

Students in physics or engineering, particularly those studying heat transfer, thermodynamics, or materials science, will benefit from this discussion.

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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Can you show where you're getting stuck? It looks like you're going to have four equations and four unknowns.
 

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