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

Formula Used:

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

Reduced Temperature (Tr):

Critical Temperature (T'c):

Reduced Pressure (Pr):

Critical Pressure (P'c):

Clausius Parameter a:

Clausius Parameter b':

Critical Molar Volume (Vm,c):

m³/mol

Reduced Molar Volume (V'm,r):

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1. What is Reduced Molar Volume of 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 determines the reduced molar volume using the Clausius equation with reduced and critical parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V'_{m,r} \) — Reduced molar volume for real gas
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_r \) — Reduced temperature
\( T'_c \) — Critical temperature (K)
\( P_r \) — Reduced pressure
\( P'_c \) — Critical pressure (Pa)
\( a \) — Clausius parameter a
\( b' \) — Clausius parameter b
\( V_{m,c} \) — Critical molar volume (m³/mol)

3. Importance of Reduced Molar Volume Calculation

Details: This calculation is essential for understanding gas behavior under various conditions and is widely used in thermodynamics and chemical engineering.

4. Using the Calculator

Tips: Enter all required parameters. Reduced temperature and pressure are dimensionless. Critical parameters should be in their respective units.

5. Frequently Asked Questions (FAQ)

Q1: What is reduced temperature?
A: Reduced temperature is the ratio of the actual temperature to the critical temperature (Tr = T/Tc).

Q2: What is reduced pressure?
A: Reduced pressure is the ratio of the actual pressure to the critical pressure (Pr = P/Pc).

Q3: Where can I find critical parameters for gases?
A: Critical parameters are typically available in thermodynamic tables or chemical engineering references.

Q4: What are typical values for Clausius parameters?
A: These vary by substance and can be found in specialized literature or determined experimentally.

Q5: Why is the universal gas constant used?
A: The universal gas constant relates energy, temperature, and amount of substance in the ideal gas law.