Alpha-function Formula:
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Definition: The alpha-function is a temperature-dependent term in the Peng-Robinson equation of state that corrects for attractive forces between molecules.
Purpose: It helps accurately predict thermodynamic properties of real gases and liquids, especially near critical points.
The calculator uses the formula:
Where:
Explanation: The function accounts for how molecular interactions change with temperature relative to the critical point.
Details: Accurate calculation is essential for predicting vapor pressures, phase equilibria, and thermodynamic properties in chemical process design.
Tips: Enter the pure component parameter (κ), system temperature (T), and critical temperature (Tc). All values must be > 0.
Q1: What is a typical value for κ?
A: For simple fluids, κ ≈ 0.37464 + 1.54226ω - 0.26992ω², where ω is the acentric factor.
Q2: Why is the square root term important?
A: It represents the temperature dependence of molecular interactions, becoming zero at the critical temperature.
Q3: What happens when T = Tc?
A: The alpha-function becomes 1, as the square root term becomes 1 and the expression simplifies to (1 + 0)².
Q4: How does this relate to the Peng-Robinson EOS?
A: The alpha-function modifies the attraction parameter 'a' in the equation: a(T) = ac × α(T).
Q5: Can this be used for mixtures?
A: Yes, but mixing rules must be applied to κ and Tc for accurate results.