Clausius-Clapeyron Relation Validation

Overview

This document validates the analytical derivatives of the Clausius-Clapeyron relation by comparing them with finite difference derivatives computed using ForwardDiff.jl. The Clausius-Clapeyron relation describes how the saturation vapor pressure changes with temperature during phase transitions.

Purpose

The validation ensures that our analytical implementation of the Clausius-Clapeyron derivatives is mathematically correct and numerically accurate. This is critical for:

  • Saturation adjustment algorithms that rely on accurate derivatives
  • Numerical stability in thermodynamic calculations
  • Physical consistency of the thermodynamic formulation

Implementation

The validation compares two approaches:

  1. Analytical derivatives: Direct computation using the derived mathematical expressions
  2. Finite difference derivatives: Numerical approximation using ForwardDiff.jl
include("Clausius_Clapeyron.jl")
"/home/runner/work/Thermodynamics.jl/Thermodynamics.jl/docs/build/Clausius_Clapeyron.svg"

Results

The plot shows:

  • Top panel: Comparison of analytical vs. finite difference derivatives
  • Middle panel: Error between the two methods
  • Bottom panel: Saturation vapor pressure as a function of temperature

Interpretation

  • Agreement: The analytical and finite difference derivatives should closely match
  • Error analysis: The middle panel shows the difference between methods
  • Physical range: The temperature range covers typical atmospheric conditions
  • Validation: Small errors indicate correct implementation
Implementation Note

This script is currently decoupled from the test suite implementation. Consider unifying the validation code with the test suite to ensure that tests and plots remain synchronized.