Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters Calculator

Critical Pressure Formula:

\[ P_c = \frac{\left(\frac{[R] \times T}{V_m - b_{PR}}\right) - \left(\frac{a_{PR} \times \alpha}{V_m^2 + 2 \times b_{PR} \times V_m - b_{PR}^2}\right)}{P_r} \]

Temperature (T):

Molar Volume (V_m):

m³/mol

Peng-Robinson Parameter b:

Peng-Robinson Parameter a:

α-function:

Reduced Pressure (P_r):

Critical Pressure (P_c):

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1. What is Critical Pressure of Real Gas?

Definition: Critical pressure is the minimum pressure required to liquefy a substance at its critical temperature.

Purpose: This calculator determines the critical pressure using the Peng-Robinson equation of state, which provides more accurate results for real gases compared to ideal gas laws.

2. How Does the Calculator Work?

The calculator uses the Peng-Robinson equation:

\[ P_c = \frac{\left(\frac{[R] \times T}{V_m - b_{PR}}\right) - \left(\frac{a_{PR} \times \alpha}{V_m^2 + 2 \times b_{PR} \times V_m - b_{PR}^2}\right)}{P_r} \]

Where:

\( P_c \) — Critical pressure (Pascal)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (Kelvin)
\( V_m \) — Molar volume (m³/mol)
\( b_{PR} \) — Peng-Robinson parameter b
\( a_{PR} \) — Peng-Robinson parameter a
\( \alpha \) — α-function (temperature-dependent)
\( P_r \) — Reduced pressure (dimensionless)

3. Importance of Critical Pressure Calculation

Details: Accurate critical pressure determination is essential for phase behavior prediction, process design in chemical engineering, and thermodynamic property calculations.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure temperature is in Kelvin and molar volume in cubic meters per mole. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Peng-Robinson equation?
A: A cubic equation of state that describes the relationship between pressure, volume, and temperature for real gases.

Q2: How do I determine Peng-Robinson parameters a and b?
A: These are substance-specific parameters typically calculated from critical properties and acentric factor.

Q3: What is the α-function?
A: A temperature-dependent function that accounts for molecular interactions, often related to the acentric factor.

Q4: Why use reduced pressure?
A: Reduced pressure (actual pressure divided by critical pressure) helps generalize the equation for different substances.

Q5: What are typical units for this calculation?
A: Temperature in Kelvin, volume in m³/mol, pressure in Pascals. The calculator outputs pressure in Pascals.