Berthelot Parameter b of Real Gas given Critical and Reduced Parameters Calculator

Berthelot Parameter b Formula:

\[ b = (V_{m,r} \times V_{m,c}) - \frac{[R] \times (T_r \times T_c)}{(P_r \times P_c) + \frac{a}{(T_r \times T_c) \times (V_{m,r} \times V_{m,c})^2}} \]

Reduced Molar Volume:

Critical Molar Volume (m³/mol):

Reduced Temperature:

Critical Temperature (K):

Reduced Pressure:

Critical Pressure (Pa):

Berthelot Parameter a:

Berthelot Parameter b:

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1. What is Berthelot Parameter b?

Definition: Berthelot parameter b is an empirical parameter characteristic to equation obtained from Berthelot model of real gas.

Purpose: It's used in the Berthelot equation of state to describe the behavior of real gases, accounting for molecular volume and intermolecular forces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = (V_{m,r} \times V_{m,c}) - \frac{[R] \times (T_r \times T_c)}{(P_r \times P_c) + \frac{a}{(T_r \times T_c) \times (V_{m,r} \times V_{m,c})^2}} \]

Where:

\( b \) — Berthelot parameter b
\( V_{m,r} \) — Reduced molar volume
\( V_{m,c} \) — Critical molar volume (m³/mol)
\( T_r \) — Reduced temperature
\( T_c \) — Critical temperature (K)
\( P_r \) — Reduced pressure
\( P_c \) — Critical pressure (Pa)
\( a \) — Berthelot parameter a
\( [R] \) — Universal gas constant (8.314 J/mol·K)

3. Importance of Berthelot Parameters

Details: The Berthelot equation provides a more accurate description of real gas behavior than the ideal gas law, especially at high pressures and low temperatures.

4. Using the Calculator

Tips: Enter all required parameters. Reduced quantities are dimensionless. Critical properties are substance-specific and must be in consistent units.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Berthelot parameters?
A: Parameters vary by substance. For example, for nitrogen: a ≈ 0.136 Pa·m⁶/mol², b ≈ 3.86×10⁻⁵ m³/mol.

Q2: How do I find critical properties of a substance?
A: Critical properties are tabulated in chemical engineering handbooks or thermodynamic databases.

Q3: What's the difference between reduced and actual properties?
A: Reduced properties are dimensionless ratios of actual properties to critical properties.

Q4: Can this calculator be used for any gas?
A: Yes, but you need the correct critical properties and Berthelot parameter a for the specific gas.

Q5: What are the limitations of the Berthelot equation?
A: It works best at moderate pressures and temperatures, and may not be accurate near the critical point.