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

Pressure Formula:

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

Reduced Temperature (T_r):

Critical Temperature For Clausius Model (T'_c):

Reduced Molar Volume for Real Gas (V'_m,r):

Critical Molar Volume (V_m,c):

m³/mol

Clausius Parameter b for Real Gas (b'):

m³/mol

Clausius Parameter a:

Pa·m⁶·K⁰·⁵/mol²

Clausius Parameter c:

m³/mol

Pressure (Pa):

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

Definition: This calculator computes the pressure of a real gas using the Clausius equation of state, which accounts for molecular size and intermolecular forces.

Purpose: It helps chemists and engineers accurately predict gas behavior under various conditions, especially near critical points.

2. How Does the Calculator Work?

The calculator uses the Clausius equation:

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

Where:

\( p \) — Pressure (Pascal)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_r \) — Reduced temperature (dimensionless)
\( T'_c \) — Critical temperature (Kelvin)
\( V'_{m,r} \) — Reduced molar volume (dimensionless)
\( V_{m,c} \) — Critical molar volume (m³/mol)
\( b' \) — Clausius parameter b (m³/mol)
\( a \) — Clausius parameter a (Pa·m⁶·K⁰·⁵/mol²)
\( c \) — Clausius parameter c (m³/mol)

Explanation: The first term accounts for molecular volume exclusion, while the second term accounts for intermolecular attractive forces.

3. Importance of Clausius Equation

Details: The Clausius equation provides more accurate pressure predictions for real gases than the ideal gas law, especially at high pressures and low temperatures.

4. Using the Calculator

Tips: Enter all required parameters. Reduced temperature and volume are dimensionless ratios. Critical parameters and Clausius parameters are substance-specific.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Clausius parameters?
A: Parameters vary by substance. For example, for CO₂: a ≈ 0.3658 Pa·m⁶·K⁰·⁵/mol², b ≈ 4.28×10⁻⁵ m³/mol, c ≈ 4.34×10⁻⁵ m³/mol.

Q2: How do I obtain reduced temperature and volume?
A: Reduced temperature = T/Tc, Reduced volume = Vm/Vm,c, where T and Vm are actual temperature and molar volume.

Q3: Why does this equation work better than ideal gas law?
A: It accounts for finite molecular size (b parameter) and intermolecular forces (a parameter), which become significant for real gases.

Q4: What's the range of validity for this equation?
A: It works well for moderate pressures and temperatures, especially near the critical point.

Q5: How accurate is this calculator?
A: Accuracy depends on the precision of input parameters and how well the Clausius equation models your specific gas.