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

Critical Pressure Formula:

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

Temperature of Real Gas:

Molar Volume:

m³/mol

Clausius Parameter b:

Clausius Parameter a:

Clausius Parameter c:

Pressure:

Critical Pressure of Real Gas (Pa):

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1. What is Critical Pressure of Real Gas?

Definition: Critical Pressure of Real Gas is the minimum pressure required to liquify a substance at the critical temperature.

Purpose: This calculator determines the critical pressure using the Clausius equation with actual and critical parameters.

2. How Does the Calculator Work?

The calculator uses the Clausius equation:

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

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
\( p \) — Pressure (Pa)

3. Importance of Critical Pressure Calculation

Details: Critical pressure is essential for understanding phase behavior and designing processes involving real gases at high pressures.

4. Using the Calculator

Tips: Enter all parameters in the specified units. Temperature, molar volume, and pressure must be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Clausius parameters?
A: Parameters a, b, and c are substance-specific and must be determined experimentally for each gas.

Q2: Why is the universal gas constant used?
A: The universal gas constant relates energy, temperature, and amount of substance in the ideal gas law.

Q3: What's the difference between critical pressure and actual pressure?
A: Critical pressure is a substance property, while actual pressure is the current system pressure.

Q4: Can this calculator be used for all gases?
A: Yes, but accurate results require correct Clausius parameters for the specific gas.

Q5: What happens at the critical point?
A: At the critical point, liquid and gas phases become indistinguishable.