Thermodynamics, Linear Interpolation

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SUMMARY

This discussion focuses on the application of linear interpolation in thermodynamics, specifically for extracting data from thermodynamic charts. The formula for linear interpolation is provided, which connects two points (x1, y1) and (x2, y2) using the equation y - y1 = m (x - x1), where m represents the slope. The derived formula for calculating y3, the interpolated value at x3, is y3 = y1 + (x3 - x1) (y2 - y1)/(x2 - x1). This method is essential for accurately estimating values between known data points in thermodynamic analysis.

PREREQUISITES
  • Understanding of basic thermodynamics concepts
  • Familiarity with linear equations and slope calculations
  • Ability to read and interpret thermodynamic charts
  • Knowledge of mathematical interpolation techniques
NEXT STEPS
  • Study the principles of thermodynamic charts and their applications
  • Learn advanced interpolation techniques beyond linear interpolation
  • Explore software tools for thermodynamic analysis, such as MATLAB or Python libraries
  • Practice solving thermodynamic problems using linear interpolation
USEFUL FOR

Students in engineering or physics, educators teaching thermodynamics, and professionals involved in thermodynamic analysis who require precise data extraction methods.

CursedAntagonis
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Homework Statement


I have been trying to learn how to use linear interpolation to find out the data needed from the thermodynamics chart, however, the book that is assigned does not even talk about it. Could someone please explain how linear interpolation is used? Thanks
 
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The assumption with linear interpolation is that the two points (x1, y1) and (x2, y2) are connected with a line. Using the two point equation of a line, we get:

y - y1 = m (x - x1), where m = (y2 - y1)/(x2 - x1)

Thus for x3 that is between x1 and x2, we get:

y3 = y1 + (x3 - x1) (y2 - y1)/(x2 - x1)
 

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