Phase Diagram Plotter
Phase Diagram Plotter creates P-V, T-S, or P-T diagrams for systems like ideal gas, using thermodynamic relations to visualize phase behavior.
Phase Diagram Overview
Phase diagrams visualize thermodynamic phase boundaries using relations like the Maxwell relation for internal energy:
Internal Energy (\(U\)): \( dU = T dS – P dV \)
Maxwell Relation:
\[ \left( \frac{\partial T}{\partial V} \right)_S = -\left( \frac{\partial P}{\partial S} \right)_V \]For an ideal gas, this relates to:
\[ \left( \frac{\partial P}{\partial T} \right)_V = \frac{nR}{V} \]Where:
- \(T\): Temperature (K)
- \(S\): Entropy (kJ/(mol·K))
- \(P\): Pressure (bar)
- \(V\): Volume (L/mol)
- \(n\): Moles (mol)
- \(R\): Gas constant (kJ/(mol·K))
Example Calculation for Ideal Gas
Example: Ideal Gas with \(n = 1 \, \text{mol}, R = 0.008314 \, \text{kJ/(mol·K)}, T = 298 \, \text{K}, V = 22.4 \, \text{L/mol}\)
Equation: \( P = \frac{nRT}{V} \)
Maxwell Relation: \(\left( \frac{\partial T}{\partial V} \right)_S = -\left( \frac{\partial P}{\partial S} \right)_V\)
Derived: \(\left( \frac{\partial P}{\partial T} \right)_V = \frac{nR}{V} = \frac{1 \times 0.008314}{22.4} \approx 0.000371 \, \text{bar/K}\)