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

Pressure Formula:

\[ p = \frac{[R] \times (T_r \times T_c)}{(V_{m,r} \times V_{m,c} - b_{PR})} - \frac{a_{PR} \times \alpha}{(V_{m,r} \times V_{m,c})^2 + 2 \times b_{PR} \times (V_{m,r} \times V_{m,c}) - b_{PR}^2} \]

Reduced Temperature (T_r):

Critical Temperature (T_c):

Reduced Molar Volume (V_m,r):

Critical Molar Volume (V_m,c):

m³/mol

Peng-Robinson Parameter b:

Peng-Robinson Parameter a:

α-function:

Pressure (Pa):

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1. What is the Peng-Robinson Equation?

Definition: The Peng-Robinson equation is a thermodynamic equation of state that provides accurate predictions of the behavior of real gases.

Purpose: It's widely used in chemical engineering and thermodynamics to calculate properties of pure components and mixtures.

2. How Does the Calculator Work?

The calculator uses the Peng-Robinson equation:

\[ p = \frac{[R] \times (T_r \times T_c)}{(V_{m,r} \times V_{m,c} - b_{PR})} - \frac{a_{PR} \times \alpha}{(V_{m,r} \times V_{m,c})^2 + 2 \times b_{PR} \times (V_{m,r} \times V_{m,c}) - b_{PR}^2} \]

Where:

\( p \) — Pressure (Pa)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_r \) — Reduced temperature (dimensionless)
\( T_c \) — Critical temperature (K)
\( V_{m,r} \) — Reduced molar volume (dimensionless)
\( V_{m,c} \) — Critical molar volume (m³/mol)
\( b_{PR} \) — Peng-Robinson parameter b
\( a_{PR} \) — Peng-Robinson parameter a
\( \alpha \) — α-function (temperature-dependent)

3. Importance of Peng-Robinson Equation

Details: This equation provides more accurate predictions of vapor pressures and liquid densities than simpler equations of state, especially near the critical point.

4. Using the Calculator

Tips: Enter all required parameters. Reduced parameters are dimensionless ratios (actual value/critical value). Critical parameters are substance-specific properties.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for a and b parameters?
A: These vary by substance. For example, for water: a ≈ 0.5536 Pa·m⁶/mol², b ≈ 3.049×10⁻⁵ m³/mol.

Q2: How is the α-function determined?
A: It's typically a function of temperature and acentric factor, often calculated as α = [1 + κ(1 - √(T_r))]² where κ is substance-specific.

Q3: When is this equation most useful?
A: For calculating properties of non-polar or slightly polar fluids at conditions near or above critical point.

Q4: What are reduced properties?
A: Reduced properties are dimensionless ratios of actual properties to critical properties (e.g., T_r = T/T_c).

Q5: How accurate is this equation?
A: Typically within 1-2% for vapor pressures and 2-5% for liquid densities for many substances.