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

Formula Used:

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

Temperature of Real Gas:

Pressure:

Clausius Parameter a:

Clausius Parameter b:

Reduced Molar Volume:

Critical Molar Volume (m³/mol):

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1. What is Critical Molar Volume?

Definition: Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.

Purpose: This calculator helps determine the critical molar volume using the Clausius equation with reduced and actual parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V_{RP} \) — Critical molar volume (m³/mol)
\( [R] \) — 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
\( V'_{m,r} \) — Reduced molar volume

3. Importance of Critical Molar Volume

Details: Critical properties are essential for understanding gas behavior under extreme conditions and for designing industrial processes.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Temperature must be in Kelvin, pressure in Pascals.

5. Frequently Asked Questions (FAQ)

Q1: What is the Clausius equation?
A: An equation of state that describes the behavior of real gases, accounting for molecular size and intermolecular forces.

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

Q3: What is reduced molar volume?
A: It's the actual molar volume divided by the critical molar volume of the substance.

Q4: Why is critical molar volume important?
A: It helps determine the state of a substance and is used in corresponding states theory for property estimation.

Q5: Can this calculator be used for all gases?
A: Yes, but accuracy depends on having correct Clausius parameters for the specific gas.