Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Actual Parameters Calculator

Formula Used:

\[ V'_{m,r} = \frac{\left(\frac{[R] \times T_{rg}}{p + \frac{a}{T_{rg}}}\right) + b'}{V_m} \]

Temperature of Real Gas:

Pressure:

Clausius Parameter a:

Clausius Parameter b:

Molar Volume:

m³/mol

Reduced Molar Volume for Real Gas:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Reduced Molar Volume for Real Gas?

Definition: Reduced Molar Volume for Real Gas of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.

Purpose: This calculator helps determine the reduced molar volume of real gases using the Clausius equation, which accounts for deviations from ideal gas behavior.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V'_{m,r} = \frac{\left(\frac{[R] \times T_{rg}}{p + \frac{a}{T_{rg}}}\right) + b'}{V_m} \]

Where:

\( V'_{m,r} \) — Reduced Molar Volume for Real Gas
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_{rg} \) — Temperature of Real Gas (K)
\( p \) — Pressure (Pa)
\( a \) — Clausius parameter a
\( b' \) — Clausius Parameter b for Real Gas
\( V_m \) — Molar Volume (m³/mol)

3. Importance of Reduced Molar Volume Calculation

Details: Calculating reduced properties helps in comparing real gas behavior to ideal gases and is essential for accurate thermodynamic calculations in chemical engineering.

4. Using the Calculator

Tips: Enter the temperature in Kelvin, pressure in Pascals, Clausius parameters a and b, and molar volume in m³/mol. Default values are provided for common conditions.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Clausius parameters?
A: Parameters vary by gas. For example, CO₂ has a ≈ 0.401 Pa·m⁶/mol² and b ≈ 4.27×10⁻⁵ m³/mol.

Q2: Why use reduced properties?
A: Reduced properties allow comparison of different gases at equivalent states relative to their critical points.

Q3: How accurate is the Clausius equation?
A: It's moderately accurate for many real gases, especially at moderate pressures and temperatures.

Q4: What's the difference between b and b'?
A: b' is the reduced form of the b parameter, accounting for molecular volume.

Q5: When would this calculation be used?
A: In chemical process design, gas storage calculations, and thermodynamic analysis of real gas systems.