What is the solution to the absurd dilatation problem?

  • Context: Graduate 
  • Thread starter Thread starter DaTario
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the dilatation problem involving two wires made of different materials, with coefficients of linear dilatation α1 = 0.0004 and α2 = -0.0002. The challenge is to determine the lengths L1 and L2 of these wires such that L1 + L2 = 2 meters, while accounting for the effects of temperature changes on their lengths. The participants clarify that the solution is not unique unless a specific temperature is defined, as variations in temperature can lead to different proportions of lengths that still satisfy the total length constraint. The formalism used to derive these lengths must reference an initial temperature to yield a unique solution.

PREREQUISITES
  • Understanding of linear thermal expansion and contraction principles
  • Familiarity with coefficients of linear dilatation
  • Basic knowledge of algebraic equations and their applications in physics
  • Concept of temperature dependence in material properties
NEXT STEPS
  • Study the mathematical derivation of thermal expansion equations, specifically L(T) = L0 + L0 α ΔT
  • Research the implications of temperature on material properties and coefficients of expansion
  • Explore case studies involving mixed materials and their thermal behavior under varying temperatures
  • Investigate the concept of non-uniqueness in solutions to physical problems and its implications in engineering
USEFUL FOR

Students and educators in physics, materials scientists, and engineers dealing with thermal expansion problems in composite materials.

  • #31
under basic ideas, onthology properties of the concepts are hidden to many.