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

Critical Pressure Formula:

\[ P'c = \frac{\left(\frac{[R] \times T_{rg}}{V_m - b'}\right) - \left(\frac{a}{T_{rg} \times (V_m + c)^2}\right)}{P_r} \]

Temperature of Real Gas (T_rg):

Molar Volume (V_m):

m³/mol

Clausius Parameter b (b'):

Clausius Parameter a:

Clausius Parameter c:

Reduced Pressure (P_r):

Critical Pressure of Real Gas (P'_c):

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1. What is Critical Pressure of Real Gas?

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

Purpose: This calculator determines the critical pressure using the Clausius equation of state for real gases.

2. How Does the Calculator Work?

The calculator uses the Clausius equation:

\[ P'c = \frac{\left(\frac{[R] \times T_{rg}}{V_m - b'}\right) - \left(\frac{a}{T_{rg} \times (V_m + c)^2}\right)}{P_r} \]

Where:

\( P'c \) — Critical pressure of real gas (Pa)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_{rg} \) — Temperature of real gas (K)
\( V_m \) — Molar volume (m³/mol)
\( b' \) — Clausius parameter b
\( a \) — Clausius parameter a
\( c \) — Clausius parameter c
\( P_r \) — Reduced pressure (dimensionless)

3. Importance of Critical Pressure Calculation

Details: Critical pressure is essential for understanding phase behavior, designing chemical processes, and predicting gas liquefaction conditions.

4. Using the Calculator

Tips: Enter all required parameters with positive values. Default values are provided for Clausius parameters a, b, c and reduced pressure.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Clausius parameters?
A: Parameters vary by gas. For example, for CO₂: a ≈ 0.3653 Pa·m⁶/mol², b ≈ 4.28×10⁻⁵ m³/mol, c ≈ 0.0428×10⁻⁵ m³/mol.

Q2: How do I find reduced pressure?
A: Reduced pressure is the ratio of actual pressure to critical pressure (P/Pc).

Q3: What units should I use?
A: Use Kelvin for temperature, m³/mol for molar volume, and dimensionless for reduced pressure.

Q4: Why does the Clausius equation include parameters a, b, c?
A: These empirical parameters account for intermolecular forces (a), molecular volume (b), and other non-ideal gas effects (c).

Q5: What's the range of validity for this equation?
A: The Clausius equation works best at moderate pressures, not too close to the critical point.