Calculating Area of Thermal Expansion for Non-Isotropic Materials

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SUMMARY

The discussion focuses on calculating the area of thermal expansion for non-isotropic materials, specifically when a rectangular plate with dimensions l1=6.1 cm and l2=6.0 cm is heated until it forms a perfect square. The coefficients of thermal expansion are given as α1=10×10-5 K-1 for l1 and α2=40×10-5 K-1 for l2. The solution requires determining the temperature change necessary for the lengths to equalize, resulting in an area of 38 cm2 for the square.

PREREQUISITES
  • Understanding of thermal expansion coefficients
  • Familiarity with the equations of linear expansion: ΔL=αL0T
  • Knowledge of area calculation for rectangles and squares
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of thermal expansion equations for non-isotropic materials
  • Learn how to calculate temperature changes using thermal expansion coefficients
  • Explore practical applications of thermal expansion in engineering materials
  • Investigate the effects of anisotropic properties on material behavior
USEFUL FOR

This discussion is beneficial for students in materials science, mechanical engineering, and physics, particularly those studying thermal properties of materials and their applications in real-world scenarios.

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Homework Statement


A non-isotropic material is heated, fractional increase in length is different along different directions. With length l1=6.1 cm and l2=6.0 cm. In direction of l1, the coefficient expansion is [itex]\alpha[/itex]1= 10×10-5 K-1 and direction l2 is [itex]\alpha[/itex]2= 40×10-5K-1. The plate is heated until it becomes a perfect square. What is the area of the square? (The answer is 38 cm2) I just don't know how use the equations without a given temperature.


Homework Equations


ΔL=[itex]\alpha[/itex]L0T
Lx=Lx0+Lx0[itex]\alpha[/itex]ΔT
Ly=Ly0+Ly0[itex]\alpha[/itex]ΔT
A0=Lx0Ly0
A=LxLy

The Attempt at a Solution


Not sure what to do with the equations without the temperature.
 
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You need to find the temperature from the condition that the rectangular becomes square.
 

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