Reduced Pressure using Peng Robinson Equation given Reduced and Critical Parameters Calculator

Formula Used:

\[ P_r = \frac{\frac{[R] \times (T_r \times T'_c)}{(V'_r \times V'_c - b_{PR})} - \frac{a_{PR} \times \alpha}{(V'_r \times V'_c)^2 + 2 \times b_{PR} \times (V'_r \times V'_c) - b_{PR}^2}}}{P_c} \]

Reduced Temperature (T_r):

Critical Temperature (T'_c) (K):

Reduced Molar Volume (V'_r):

Critical Molar Volume (V'_c) (m³/mol):

Peng-Robinson Parameter b:

Peng-Robinson Parameter a:

α-function:

Critical Pressure (P_c) (Pa):

Reduced Pressure (P_r):

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1. What is Reduced Pressure using Peng Robinson Equation?

Definition: This calculator computes the reduced pressure using the Peng-Robinson equation of state, given reduced and critical parameters.

Purpose: It helps in thermodynamic calculations for real gases, particularly in petroleum and chemical engineering applications.

2. How Does the Calculator Work?

The calculator uses the Peng-Robinson equation:

\[ P_r = \frac{\frac{[R] \times (T_r \times T'_c)}{(V'_r \times V'_c - b_{PR})} - \frac{a_{PR} \times \alpha}{(V'_r \times V'_c)^2 + 2 \times b_{PR} \times (V'_r \times V'_c) - b_{PR}^2}}{P_c} \]

Where:

\( P_r \) — Reduced pressure (dimensionless)
\( T_r \) — Reduced temperature (dimensionless)
\( T'_c \) — Critical temperature (K)
\( V'_r \) — Reduced molar volume (dimensionless)
\( V'_c \) — Critical molar volume (m³/mol)
\( b_{PR} \) — Peng-Robinson parameter b
\( a_{PR} \) — Peng-Robinson parameter a
\( \alpha \) — α-function
\( P_c \) — Critical pressure (Pa)
\( [R] \) — Universal gas constant (8.314 J/mol·K)

3. Importance of Reduced Pressure Calculation

Details: Reduced properties are crucial for corresponding states theory and help predict thermodynamic behavior of real gases.

4. Using the Calculator

Tips: Enter all required parameters. Ensure all values are positive. Critical parameters are substance-specific.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Peng-Robinson parameters?
A: These vary by substance. For example, for water: a ≈ 0.4572 Pa·m⁶/mol², b ≈ 1.49×10⁻⁵ m³/mol.

Q2: How do I obtain critical parameters?
A: Critical parameters are tabulated for most substances in thermodynamic databases.

Q3: What is the α-function?
A: It's a temperature-dependent function that accounts for deviations from ideal behavior.

Q4: Can this be used for all gases?
A: The Peng-Robinson equation works well for non-polar and slightly polar compounds.

Q5: Why use reduced properties?
A: They allow generalized correlations that work for many substances.