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

Critical Pressure Formula:

\[ P'_c = \frac{\frac{[R] \times (T_r \times T'_c)}{(V'_{m,r} \times V_{m,c}) - b'} - \frac{a}{(T_r \times T'_c) \times ((V'_{m,r} \times V_{m,c}) + c)^2}}{P_r} \]

Reduced Temperature (Tr):

Critical Temperature (T'c) in K:

Reduced Molar Volume (V'm,r):

Critical Molar Volume (Vm,c) in m³/mol:

Clausius Parameter b':

Clausius Parameter a:

Clausius Parameter c:

Reduced Pressure (Pr):

Critical Pressure of Real Gas (Pa):

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1. What is Critical Pressure of Real Gas using Clausius Equation?

Definition: This calculator determines the critical pressure of a real gas using the Clausius equation with reduced and critical parameters.

Purpose: It helps in thermodynamic calculations and understanding gas behavior near critical conditions.

2. How Does the Calculator Work?

The calculator uses the Clausius equation:

\[ P'_c = \frac{\frac{[R] \times (T_r \times T'_c)}{(V'_{m,r} \times V_{m,c}) - b'} - \frac{a}{(T_r \times T'_c) \times ((V'_{m,r} \times V_{m,c}) + c)^2}}{P_r} \]

Where:

\( P'_c \) — Critical Pressure of Real Gas (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)
\( b' \) — 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-liquid transitions.

4. Using the Calculator

Tips: Enter all required parameters. Reduced parameters are dimensionless. Critical temperature is in Kelvin, and critical molar volume is in m³/mol.

5. Frequently Asked Questions (FAQ)

Q1: What are reduced parameters?
A: Reduced parameters are ratios of actual values to critical values (e.g., Tr = T/Tc).

Q2: How do I obtain Clausius parameters?
A: These are empirical parameters specific to each gas, typically found in thermodynamic tables.

Q3: What units does this calculator use?
A: The result is in Pascals (Pa). Inputs should be in consistent units as described.

Q4: Why use the Clausius equation?
A: It provides better accuracy for real gases compared to ideal gas law, especially near critical conditions.

Q5: What's the range of validity?
A: The equation works best near critical conditions but accuracy decreases far from these points.