Thermal expansion across a copper rod

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SUMMARY

The discussion focuses on determining the temperature distribution and resulting shape of a copper rod subjected to thermal conditions, with one end at 200°C and the other at 0°C. The rod has a diameter of 2.54 cm and a length of 0.5 meters, with a thermal conductivity of 380 J/(smC). The key equation used is the heat transfer equation, ΔQ = k A (Thot – Tcold) / Δt L, which is essential for calculating the thermal expansion and temperature gradient along the rod.

PREREQUISITES
  • Understanding of thermal conductivity and heat transfer principles
  • Familiarity with the concepts of linear and volumetric thermal expansion
  • Knowledge of the heat transfer equation and its components
  • Basic mathematical skills for solving equations involving temperature gradients
NEXT STEPS
  • Study the derivation and application of the heat transfer equation in thermal systems
  • Learn about the principles of linear and volumetric expansion in materials
  • Explore numerical methods for solving temperature distribution problems
  • Investigate the thermal properties of different materials for comparative analysis
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Students in physics or engineering, particularly those studying thermodynamics and heat transfer, as well as professionals involved in materials science and thermal analysis.

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Homework Statement



Determine the actual shape of a copper bar in contact with a furnace at a constant 200 C at one end and a constant ice bank at 0 C at the other end.

Diameter of the rod is 2.54 cm. Length is .5 meters. Thermal conductivity of copper is 380 J /
(smC)

Homework Equations




Q = k A (Thot – Tcold)
t L

The Attempt at a Solution



Honestly, I have no idea how to do this. I know that I must find the temperature distribution across the rod in order to find the linear and volumetric expansion at each point. But I don't know how to do this.
 
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bump. someone please help.
 

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